TALAPRASTHARA ( Combinatorics)

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 x 47
#51
8th part:
Examples:
Panchanganashta:
1.What is the series of Angas pertaining to the 1st prastara of 6Drutapermutation (6DP) of Panchangaprastara (2619/1  among them while â€˜2â€™ represents Panchangaprastara, â€˜6â€™ represents the total number of units of the permutation 6DP, â€˜19â€™ represents the respective Sankhya and the last â€˜1â€™represents the questionnumber)?
To write the Sankhya of Panchangaprastara, the total of the existing figures of the preceding 1st, 2nd, 4th, 6th and 8th houses, which are the respective proxies of Panchangaprastara, should be written and now, as per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜1â€™ from the Sankhya figure â€˜19â€™ of 6DP and the remainder is (191=) 18.
From the above remainder â€˜18â€™, as the 1st, 2nd and 4th proxies could consecutively be subtracted (1810=86=22=0) consider the nonsubtraction of the 6th proxy â€˜1â€™ and write the Anga, Pluta of the same proxy as per rule No.3. Thus, this prastara consists of â€˜Śâ€™.
2.What is the series of Angas pertaining to the 2nd prastara of 6DP of Panchangaprastara (2619/2)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜2â€™ from the Sankhya figure 19 of 6DP and the remainder is (192=) 17.
Later, from the above remainder â€˜17â€™, as the 1st and 2nd proxies could consecutively be subtracted (1710=76=1) consider the nonsubtraction of the 4th proxy â€˜2â€™ and write its Anga, Guru as per rule No.3 leaving away its figure â€˜2â€™ to continue the process.
Later, from the last remainder â€˜1â€™, as the 1st proxy of the last leftoff proxy â€˜2â€™ could be subtracted (11=0) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of â€˜l Sâ€™.
3.What is the series of Angas pertaining to the 3rd prastara of 6DP of Panchangaprastara (2619/3)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜3â€™ from the Sankhya figure 19 of 6DP and the remainder is (193=) 16.
Later, from the above remainder â€˜16â€™, as the 1st and 2nd proxies could consecutively be subtracted (1610=66=0) consider the nonsubtraction of the 4th proxy and write its Anga, Guru as per rule No.3.
Later, to fill in the deficit value of the permutation write two Drutas consecutively as per rule No.5. Thus, this prastara consists of â€˜0 0 Sâ€™.
4.What is the series of Angas pertaining to the 4th prastara of 6DP of Panchangaprastara (2619/4)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜4â€™ from the Sankhya figure 19 of 6DP and the remainder is (194=) 15.
Later, from the above remainder â€˜15â€™, as the 1st proxy only could be subtracted (1510=5) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3 leaving away its proxy â€˜6â€™ to continue the process.
Later, from the last remainder â€˜5â€™, the 1st and 2nd proxies of the last leftoff proxy â€˜6â€™ could consecutively be subtracted (53=22=0) consider the nonsubtraction of the 4th proxy and write its Anga, Guru as per rule No.3. Thus, this prastara consists of â€˜S lâ€™.
5.What is the series of Angas pertaining to the 5th prastara of 6DP of Panchangaprastara (2619/5)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜5â€™ from the Sankhya figure 19 of 6DP and the remainder is (195=) 14.
Later, from the above remainder â€˜14â€™, as the 1st proxy could be subtracted (1410=4) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3 leaving away its proxy â€˜6â€™ to continue the process.
Later, from the last remainder â€˜4â€™, as the 1st proxy â€˜3â€™ of the last leftoff proxy â€˜6â€™ could be subtracted (43=1) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3 leaving away its proxy â€˜2â€™ to continue the process.
Later, from the last remainder â€˜1â€™, as the 1st proxy â€˜1â€™ of the last proxy â€˜2â€™ could be subtracted (11=0) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of â€˜l l lâ€™.
6.What is the series of Angas pertaining to the 7th prastara of 6DP of Panchangaprastara (2619/7)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜5â€™ from the Sankhya figure 19 of 6DP and the remainder is (197=) 12.
Later, from the above remainder â€˜12â€™, as the 1st proxy could be subtracted (1210=2) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu leaving away its proxy â€˜6â€™ to continue the process.
Later, from the last remainder â€˜2â€™, as the 1st proxy â€˜3â€™ of the last leftoff proxy â€˜6â€™ could not be subtracted write the Anga, Druta of the same proxy as per rule No.3 to continue the process.
Later, from the last remainder â€˜2â€™, as the 1st proxy â€˜2â€™ of the last undeducted proxy â€˜3â€™ could be subtracted (22=0) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3.
Later, to fillin the deficit value of the units, write only one Druta as per rule No.5. Thus, this prastara consists of â€˜0 l 0 lâ€™.
7.What is the series of Angas pertaining to the 12th prastara of 6DP of Panchangaprastara (2619/12)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜12â€™ from the Sankhya figure 19 of 6DP and the remainder is (1912=) 7.
Later, from the above remainder â€˜7â€™, as the 1st proxy â€˜10â€™ could not be subtracted write its Anga, Druta and continue the process.
Later, from the above remainder â€˜7â€™, as the 1st proxy â€˜6â€™ of the last undeducted proxy â€˜10â€™ could be subtracted (76=1) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu leaving away its proxy â€˜3â€™ as per rule No.3 to continue the process.
Later, from the last remainder â€˜1â€™, as the 1st proxy â€˜2â€™ of the last leftoff proxy â€˜3â€™ could not be subtracted write its Anga, Druta as per rule No.3 and continue the process.
Later, from the last remainder â€˜1â€™, as the 1st proxy â€˜1â€™ of the last undeducted proxy â€˜2â€™ could be subtracted (11=0) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of â€˜l 0 l 0â€™.
8.What is the series of Angas pertaining to the 16th prastara of 6DP of Panchangaprastara (2619/16)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜16â€™ from the Sankhya figure 19 of 6DP and the remainder is (1916=) 3.
Later, from the above remainder â€˜3â€™, as the 1st proxy â€˜10â€™ and again its 1st proxy â€˜6â€™ could not be subtracted, write two Angas, Drutas of the the same 1st proxy and continue the process.
Later, from the above remainder â€˜3â€™, as the 1st proxy â€˜3â€™ of the last undeducted proxy â€˜6â€™ could be subtracted (33=0) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3
Later, to fill in the deficit value of the total units of the permutation write two Drutas as per rule No.5. Thus, this prastara consists of â€˜0 0 l 0 0â€™.
Shadanga  trisrajaati  nashta:
1.What is the series of Angas pertaining to the 15th prastara of 6Anudrutapermutation (6ADP) of Shadangatrisrajaatiprastara (3625/15)?
As per rule No.1 write the figures of Sankhya upto the required 6ADP (refer table).
Now, as per rule No.2, subtract the question number â€˜15â€™ from the Sankhya figure â€˜25â€™ of 6ADP and the remainder is (2515=) 10.
Later, from the above remainder â€˜10â€™, as the 1st proxy â€˜13â€™ could not be subtracted, write its Anga, Anudruta as per rule No.3 and continue the process.
Later, from the above remainder â€˜10â€™, as the 1st proxy â€˜7â€™ of the last undeducted proxy â€˜13â€™ could be subtracted (107=3) consider the nonsubtraction of the 2nd proxy and write its Anga, Druta leaving away its proxy â€˜4â€™ to continue the process.
Later, from the last remainder â€˜3â€™, as the 1st and 2nd proxies of the last leftoff proxy â€˜4â€™ could consecutively be subtracted (32=11=0) consider the nonsubtraction of the 3rd proxy and write its Anga, Laghu. Thus, this prastara consists of â€˜l 0 Uâ€™.
Shadanga  chaturashrajaati  nashta:
1.What is the series of Angas pertaining to the 16th prastara of 7ADP of Shadangachaturashrajaatiprastara (4731/16)?
As per rule No.1 write the figures of Sankhya upto the required 7ADP (refer table).
Now, as per rule No.2, subtract the question number â€˜16â€™ from the Sankhya figure â€˜31â€™ of 7ADP and the remainder is (3116=) 15.
Later, from the above remainder â€˜15â€™, as the 1st proxy â€˜18â€™ could not be subtracted, write its Anga, Anudruta as per rule No.3 and continue the process.
Later, from the above remainder â€˜15â€™, as the 1st proxy â€˜10â€™ of the last undeducted proxy â€˜18â€™ could be subtracted (1510=5), consider the nonsubtraction of the 2nd proxy and write its Anga, Druta leaving away its proxy â€˜6â€™ as per rule No.3 to continue the process.
Later, from the last remainder â€˜5â€™, as the 1st and 2nd proxies of the last leftoff proxy â€˜6â€™ could consecutively be subtracted (53=22=0) consider the nonsubtraction of the 4th proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of â€˜l 0 Uâ€™.
Shadanga  khanda  jaati  nashta :
1.What is the series of Angas pertaining to the 3rd prastara of 7ADP of Shadangakhandajaatiprastara (5726/3)?
As per rule No.1 write the figures of Sankhya upto the required 7ADP (refer table).
Now, as per rule No.2, subtract the question number â€˜3â€™ from the Sankhya figure â€˜26â€™ of 7ADP and the remainder is (263=) 23.
Later, from the above remainder â€˜23â€™, as the 1st proxy could be subtracted (2315=8) consider the nonsubtraction of the 2nd proxy and write its Anga, Druta leaving away its proxy â€˜9â€™ as per rule No.3 to continue the process.
Later, from the last remainder â€˜8â€™, as the 1st and 2nd proxies of the last leftoff proxy â€˜9â€™ could consecutively be subtracted (85=33=0) consider the nonsubtraction of the 5th proxy and write its Anga, Laghu. Thus, this prastara consists of â€˜l 0â€™.
Shadanga  mishra  jaati  nashta :
1.What is the series of Angas pertaining to the 1st prastara of 8ADP of Shadangamishrajaatiprastara (8736/1)?
As per rule No.1 write the figures of Sankhya upto the required 8ADP (refer table).
Now, as per rule No.2, subtract the question number â€˜1â€™ from the Sankhya figure â€˜36â€™ of 8ADP and the remainder is (361=) 35.
Later, from the above remainder â€˜35â€™, as the 1st and 2nd proxies could consecutively be subtracted (3522=1313=0) consider the nonsubtraction of the 7th proxy and write its Anga, Laghu as per rule No.3.
Later, to fill in the deficit value of units of the permutation write one Anudruta as per rule No.5. Thus, this prastara consists of â€˜U lâ€™.
Shadanga  sankeerna  jaati  nashta :
1.What is the series of Angas pertaining to the 1st prastara of 9ADP of Shadangasankeernajaatiprastara (9956/1)?
As per rule No.1 write the figures of Sankhya upto the required 9ADP (refer table).
Now, as per rule No.2, subtract the question number â€˜1â€™ from the Sankhya figure â€˜56â€™ of 9ADP and the remainder is (561=) 55.
Later, from the above remainder â€˜55â€™, as the 1st and 2nd proxies could consecutively be subtracted (5534=2121=0) consider the nonsubtraction of the 9th proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of â€˜lâ€™.
In the same manner the respective Nashta of other permutations should also be answered basing upon the respective proxies.
Examples:
Panchanganashta:
1.What is the series of Angas pertaining to the 1st prastara of 6Drutapermutation (6DP) of Panchangaprastara (2619/1  among them while â€˜2â€™ represents Panchangaprastara, â€˜6â€™ represents the total number of units of the permutation 6DP, â€˜19â€™ represents the respective Sankhya and the last â€˜1â€™represents the questionnumber)?
To write the Sankhya of Panchangaprastara, the total of the existing figures of the preceding 1st, 2nd, 4th, 6th and 8th houses, which are the respective proxies of Panchangaprastara, should be written and now, as per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜1â€™ from the Sankhya figure â€˜19â€™ of 6DP and the remainder is (191=) 18.
From the above remainder â€˜18â€™, as the 1st, 2nd and 4th proxies could consecutively be subtracted (1810=86=22=0) consider the nonsubtraction of the 6th proxy â€˜1â€™ and write the Anga, Pluta of the same proxy as per rule No.3. Thus, this prastara consists of â€˜Śâ€™.
2.What is the series of Angas pertaining to the 2nd prastara of 6DP of Panchangaprastara (2619/2)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜2â€™ from the Sankhya figure 19 of 6DP and the remainder is (192=) 17.
Later, from the above remainder â€˜17â€™, as the 1st and 2nd proxies could consecutively be subtracted (1710=76=1) consider the nonsubtraction of the 4th proxy â€˜2â€™ and write its Anga, Guru as per rule No.3 leaving away its figure â€˜2â€™ to continue the process.
Later, from the last remainder â€˜1â€™, as the 1st proxy of the last leftoff proxy â€˜2â€™ could be subtracted (11=0) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of â€˜l Sâ€™.
3.What is the series of Angas pertaining to the 3rd prastara of 6DP of Panchangaprastara (2619/3)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜3â€™ from the Sankhya figure 19 of 6DP and the remainder is (193=) 16.
Later, from the above remainder â€˜16â€™, as the 1st and 2nd proxies could consecutively be subtracted (1610=66=0) consider the nonsubtraction of the 4th proxy and write its Anga, Guru as per rule No.3.
Later, to fill in the deficit value of the permutation write two Drutas consecutively as per rule No.5. Thus, this prastara consists of â€˜0 0 Sâ€™.
4.What is the series of Angas pertaining to the 4th prastara of 6DP of Panchangaprastara (2619/4)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜4â€™ from the Sankhya figure 19 of 6DP and the remainder is (194=) 15.
Later, from the above remainder â€˜15â€™, as the 1st proxy only could be subtracted (1510=5) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3 leaving away its proxy â€˜6â€™ to continue the process.
Later, from the last remainder â€˜5â€™, the 1st and 2nd proxies of the last leftoff proxy â€˜6â€™ could consecutively be subtracted (53=22=0) consider the nonsubtraction of the 4th proxy and write its Anga, Guru as per rule No.3. Thus, this prastara consists of â€˜S lâ€™.
5.What is the series of Angas pertaining to the 5th prastara of 6DP of Panchangaprastara (2619/5)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜5â€™ from the Sankhya figure 19 of 6DP and the remainder is (195=) 14.
Later, from the above remainder â€˜14â€™, as the 1st proxy could be subtracted (1410=4) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3 leaving away its proxy â€˜6â€™ to continue the process.
Later, from the last remainder â€˜4â€™, as the 1st proxy â€˜3â€™ of the last leftoff proxy â€˜6â€™ could be subtracted (43=1) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3 leaving away its proxy â€˜2â€™ to continue the process.
Later, from the last remainder â€˜1â€™, as the 1st proxy â€˜1â€™ of the last proxy â€˜2â€™ could be subtracted (11=0) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of â€˜l l lâ€™.
6.What is the series of Angas pertaining to the 7th prastara of 6DP of Panchangaprastara (2619/7)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜5â€™ from the Sankhya figure 19 of 6DP and the remainder is (197=) 12.
Later, from the above remainder â€˜12â€™, as the 1st proxy could be subtracted (1210=2) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu leaving away its proxy â€˜6â€™ to continue the process.
Later, from the last remainder â€˜2â€™, as the 1st proxy â€˜3â€™ of the last leftoff proxy â€˜6â€™ could not be subtracted write the Anga, Druta of the same proxy as per rule No.3 to continue the process.
Later, from the last remainder â€˜2â€™, as the 1st proxy â€˜2â€™ of the last undeducted proxy â€˜3â€™ could be subtracted (22=0) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3.
Later, to fillin the deficit value of the units, write only one Druta as per rule No.5. Thus, this prastara consists of â€˜0 l 0 lâ€™.
7.What is the series of Angas pertaining to the 12th prastara of 6DP of Panchangaprastara (2619/12)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜12â€™ from the Sankhya figure 19 of 6DP and the remainder is (1912=) 7.
Later, from the above remainder â€˜7â€™, as the 1st proxy â€˜10â€™ could not be subtracted write its Anga, Druta and continue the process.
Later, from the above remainder â€˜7â€™, as the 1st proxy â€˜6â€™ of the last undeducted proxy â€˜10â€™ could be subtracted (76=1) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu leaving away its proxy â€˜3â€™ as per rule No.3 to continue the process.
Later, from the last remainder â€˜1â€™, as the 1st proxy â€˜2â€™ of the last leftoff proxy â€˜3â€™ could not be subtracted write its Anga, Druta as per rule No.3 and continue the process.
Later, from the last remainder â€˜1â€™, as the 1st proxy â€˜1â€™ of the last undeducted proxy â€˜2â€™ could be subtracted (11=0) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of â€˜l 0 l 0â€™.
8.What is the series of Angas pertaining to the 16th prastara of 6DP of Panchangaprastara (2619/16)?
As per rule No.1 write the figures of Sankhya upto the required 6DP (refer table).
Now, as per rule No.2, subtract the question number â€˜16â€™ from the Sankhya figure 19 of 6DP and the remainder is (1916=) 3.
Later, from the above remainder â€˜3â€™, as the 1st proxy â€˜10â€™ and again its 1st proxy â€˜6â€™ could not be subtracted, write two Angas, Drutas of the the same 1st proxy and continue the process.
Later, from the above remainder â€˜3â€™, as the 1st proxy â€˜3â€™ of the last undeducted proxy â€˜6â€™ could be subtracted (33=0) consider the nonsubtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3
Later, to fill in the deficit value of the total units of the permutation write two Drutas as per rule No.5. Thus, this prastara consists of â€˜0 0 l 0 0â€™.
Shadanga  trisrajaati  nashta:
1.What is the series of Angas pertaining to the 15th prastara of 6Anudrutapermutation (6ADP) of Shadangatrisrajaatiprastara (3625/15)?
As per rule No.1 write the figures of Sankhya upto the required 6ADP (refer table).
Now, as per rule No.2, subtract the question number â€˜15â€™ from the Sankhya figure â€˜25â€™ of 6ADP and the remainder is (2515=) 10.
Later, from the above remainder â€˜10â€™, as the 1st proxy â€˜13â€™ could not be subtracted, write its Anga, Anudruta as per rule No.3 and continue the process.
Later, from the above remainder â€˜10â€™, as the 1st proxy â€˜7â€™ of the last undeducted proxy â€˜13â€™ could be subtracted (107=3) consider the nonsubtraction of the 2nd proxy and write its Anga, Druta leaving away its proxy â€˜4â€™ to continue the process.
Later, from the last remainder â€˜3â€™, as the 1st and 2nd proxies of the last leftoff proxy â€˜4â€™ could consecutively be subtracted (32=11=0) consider the nonsubtraction of the 3rd proxy and write its Anga, Laghu. Thus, this prastara consists of â€˜l 0 Uâ€™.
Shadanga  chaturashrajaati  nashta:
1.What is the series of Angas pertaining to the 16th prastara of 7ADP of Shadangachaturashrajaatiprastara (4731/16)?
As per rule No.1 write the figures of Sankhya upto the required 7ADP (refer table).
Now, as per rule No.2, subtract the question number â€˜16â€™ from the Sankhya figure â€˜31â€™ of 7ADP and the remainder is (3116=) 15.
Later, from the above remainder â€˜15â€™, as the 1st proxy â€˜18â€™ could not be subtracted, write its Anga, Anudruta as per rule No.3 and continue the process.
Later, from the above remainder â€˜15â€™, as the 1st proxy â€˜10â€™ of the last undeducted proxy â€˜18â€™ could be subtracted (1510=5), consider the nonsubtraction of the 2nd proxy and write its Anga, Druta leaving away its proxy â€˜6â€™ as per rule No.3 to continue the process.
Later, from the last remainder â€˜5â€™, as the 1st and 2nd proxies of the last leftoff proxy â€˜6â€™ could consecutively be subtracted (53=22=0) consider the nonsubtraction of the 4th proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of â€˜l 0 Uâ€™.
Shadanga  khanda  jaati  nashta :
1.What is the series of Angas pertaining to the 3rd prastara of 7ADP of Shadangakhandajaatiprastara (5726/3)?
As per rule No.1 write the figures of Sankhya upto the required 7ADP (refer table).
Now, as per rule No.2, subtract the question number â€˜3â€™ from the Sankhya figure â€˜26â€™ of 7ADP and the remainder is (263=) 23.
Later, from the above remainder â€˜23â€™, as the 1st proxy could be subtracted (2315=8) consider the nonsubtraction of the 2nd proxy and write its Anga, Druta leaving away its proxy â€˜9â€™ as per rule No.3 to continue the process.
Later, from the last remainder â€˜8â€™, as the 1st and 2nd proxies of the last leftoff proxy â€˜9â€™ could consecutively be subtracted (85=33=0) consider the nonsubtraction of the 5th proxy and write its Anga, Laghu. Thus, this prastara consists of â€˜l 0â€™.
Shadanga  mishra  jaati  nashta :
1.What is the series of Angas pertaining to the 1st prastara of 8ADP of Shadangamishrajaatiprastara (8736/1)?
As per rule No.1 write the figures of Sankhya upto the required 8ADP (refer table).
Now, as per rule No.2, subtract the question number â€˜1â€™ from the Sankhya figure â€˜36â€™ of 8ADP and the remainder is (361=) 35.
Later, from the above remainder â€˜35â€™, as the 1st and 2nd proxies could consecutively be subtracted (3522=1313=0) consider the nonsubtraction of the 7th proxy and write its Anga, Laghu as per rule No.3.
Later, to fill in the deficit value of units of the permutation write one Anudruta as per rule No.5. Thus, this prastara consists of â€˜U lâ€™.
Shadanga  sankeerna  jaati  nashta :
1.What is the series of Angas pertaining to the 1st prastara of 9ADP of Shadangasankeernajaatiprastara (9956/1)?
As per rule No.1 write the figures of Sankhya upto the required 9ADP (refer table).
Now, as per rule No.2, subtract the question number â€˜1â€™ from the Sankhya figure â€˜56â€™ of 9ADP and the remainder is (561=) 55.
Later, from the above remainder â€˜55â€™, as the 1st and 2nd proxies could consecutively be subtracted (5534=2121=0) consider the nonsubtraction of the 9th proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of â€˜lâ€™.
In the same manner the respective Nashta of other permutations should also be answered basing upon the respective proxies.
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 Posts: 629
 Joined: 30 Jul 2006, 08:56
 x 4
#52
Dear Msakella Sir,
As you had asked, I attempted to do the Panchanga Prastara Kalita for 7UP. Please verify and let me know if I have understood this right.
Here a unit stands for 1 Drutam.
1. No 8th proxy. So no kakapadam.
2. 6th proxy. S+M=1+1=2
1 figure of S' and 1 other figure as per M
S+M indicates that there should be only 2 figures of S' in all the 33 permutations
DA: 1/O,1/S'.
3. 4th proxy S+M=3+7=10
3 figures of S. 7 other figures.
S+M=10 indicates that there are only 10 figures of S in all the permutations
DA: 2/,5/O,3/S
4. 2nd proxy. S+M=10+34=44
10, 34 other figures.
There should be only 44 laghus in all the 33 permutations.
DA : 2/S,10/,22/O,10/
5. 1st proxy. S+M=19+72=91
19 O. 72 other figures.
There should be only 91 O's in all the permutations
DA: 1/S', 5/S, 22/, 44/, 19/O
As you had asked, I attempted to do the Panchanga Prastara Kalita for 7UP. Please verify and let me know if I have understood this right.
Here a unit stands for 1 Drutam.
1. No 8th proxy. So no kakapadam.
2. 6th proxy. S+M=1+1=2
1 figure of S' and 1 other figure as per M
S+M indicates that there should be only 2 figures of S' in all the 33 permutations
DA: 1/O,1/S'.
3. 4th proxy S+M=3+7=10
3 figures of S. 7 other figures.
S+M=10 indicates that there are only 10 figures of S in all the permutations
DA: 2/,5/O,3/S
4. 2nd proxy. S+M=10+34=44
10, 34 other figures.
There should be only 44 laghus in all the 33 permutations.
DA : 2/S,10/,22/O,10/
5. 1st proxy. S+M=19+72=91
19 O. 72 other figures.
There should be only 91 O's in all the permutations
DA: 1/S', 5/S, 22/, 44/, 19/O
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#53
Dear member, sbala, It should be cited as 7DP in Panchangaprastara, 7AP in Shadangaprastara and 7UP in Samyuktangaprastara. You can get the symbol, â€˜Śâ€™ of Pluta in the â€˜Arialâ€™ of symbols in your PC and you can use that. For the symbol, Laghu you can use the alphabet small Ell â€˜lâ€™ or figure one, â€˜1â€™.
There are 3 kinds of applications of each one of these proxies and you should write down all of them as follows.
(You should write them applying to the proxies from right to left only but not from left to right)
1. (a) As per the first1st proxy there are 19 Dritantyaprastaras consisting of 72 other Angas, (b) among these 72 other Angas, apart from these 19 Drutas lying in the right extreme of each one of these 19 Drutantyaprastaras, as per the first1st proxy there are (10 + 34 =) 44 Drutas, second2nd proxy there are (6 + 16 =) 22 Laghus, third4th proxy there are (2 + 3 = ) 5 Gurus, fourth6th proxy there is only 1 Pluta arriving at a total of (44D + 22L + 5G + 1P =) 72 (c) in all these 33 permutations there are only (72 + 19 =) 91 Drutas.
In the same manner you should write to all the respective proxies. Proceed.
Also go through the 7th chapter of my book â€˜Indian genius in Talaprastaraâ€™ and tally the matter furnished in my another book â€˜Systematisation of Prastara details of Deshi Talasâ€™. amsharma.
There are 3 kinds of applications of each one of these proxies and you should write down all of them as follows.
(You should write them applying to the proxies from right to left only but not from left to right)
1. (a) As per the first1st proxy there are 19 Dritantyaprastaras consisting of 72 other Angas, (b) among these 72 other Angas, apart from these 19 Drutas lying in the right extreme of each one of these 19 Drutantyaprastaras, as per the first1st proxy there are (10 + 34 =) 44 Drutas, second2nd proxy there are (6 + 16 =) 22 Laghus, third4th proxy there are (2 + 3 = ) 5 Gurus, fourth6th proxy there is only 1 Pluta arriving at a total of (44D + 22L + 5G + 1P =) 72 (c) in all these 33 permutations there are only (72 + 19 =) 91 Drutas.
In the same manner you should write to all the respective proxies. Proceed.
Also go through the 7th chapter of my book â€˜Indian genius in Talaprastaraâ€™ and tally the matter furnished in my another book â€˜Systematisation of Prastara details of Deshi Talasâ€™. amsharma.
Last edited by msakella on 29 Jan 2007, 21:12, edited 1 time in total.
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#54
9th part:
KHANDAPRASTARA
The process of Khandaprastara should also be made following the same rules of Akhandaprastara but observing some restrictions like devoid or containing a particular Anga. This is of two kinds and they are namely 1.Heenaprastara (Devoidpermutation), this is Angaheenaprastara in which the process of permutation should be made devoid of a particular Anga and 2.Yuktaprastara (Containingpermutation), this is like Ekangayuktaprastara, Dviyangayuktaprastara, Triangayuktaprastara and so on in which the process of permutation should be made containing a particular number of a particular Anga ( among them the word â€˜Angaâ€™ should be replaced with the name of an Anga among the six Talangas or â€˜Amshaâ€™ or unit like Anudrutaheenaprastara, Drutaheenaprastara of the respective Panchanga & Shadangaprastaras, Ekamshaheenaprastara, Dviamshaheenaprastara of Samyuktangaprastara of Heenaprastara, Ekanudrutayuktaprastara, Dvianudrutayuktaprastara, Tridrutayuktaprastara, Chaturlaghuyuktaprastara of the respective Panchanga & Shadangaprastaras and Ekaekamshayuktaprastara, Dviekamshayuktaprastara, Tridviamshayuktaprastara, Chaturchaturamshayuktaprastara of Samyuktangaprastara and so on of Yuktaprastara.
Example: If you carefully observe the 33 Akandaprastaras of 7DP you will find that Drutaheenaprastaras are â€˜0â€™, Ekadrutayuktaprastaras are â€˜12â€™, Tridrutayuktaprastaras are â€˜14â€™, Panchadrutayuktaprastaras are â€˜5â€™ and Saptadrutaprastara is â€˜1â€™ in Khandaprastara arriving at the total (12 + 14 + 6 + 1 =) 33. The same should be applied to all.
271012
0 Ś  01
0 l S  02
l 0 S  03
0 S l  04
0 l l l  05
l 0 l l  06
S 0 l  07
l l 0 l  08
Ś 0  09
l S 0 10
S l 0  11
l l l 0  12
271114
0 0 0 S  01
0 0 0 l l  02
0 0 l 0 l  03
0 l 0 0 l  04
l 0 0 0 l  05
0 0 S 0  06
0 0 l l 0  07
0 l 0 l 0  08
l 0 0 l 0  09
0 S 0 0  10
0 l l 0 0  11
l 0 l 0 0  12
S 0 0 0  13
l l 0 0 0  14
27156
0 0 0 0 0 l  01
0 0 0 0 l 0  02
0 0 0 l 0 0  03
0 0 l 0 0 0  04
0 l 0 0 0 0  05
l 0 0 0 0 0  06
27171
0 0 0 0 0 0 0  01
Like the â€˜Table of general permutationsâ€™ bringing out the details of Sankhya and Mahapatala of all the units of permutations of Akhandaprastara, in Khandaprastara, to bring out the details of the respective Sankhya and Mahapatala of Heenaprastara and Yuktaprastara of all respective Angas independent tables of each and every Anga have to be prepared. Thus, in Panchangaprastara, where five Angas are used in the process of permutation, an independent table to each of these five Angas have to be prepared, in Shadangaprastara, where six Angas are used in the process of permutation, six tables have to be prepared and in Samyuktangaprastara, depending upon the desired units of permutation, an independent table to each increasedunit should be prepared. For example please go through the item â€˜2.3.2.Khandaprastara and 2.4.Tables of angas and their applicationâ€™ in page 10 and the different tables of Druta, Laghu, Guru, Pluta and Kakapada of Panchangaprastara in Chapter3 of my book â€˜Indian genius in Talaprastaraâ€™. amsharma.
KHANDAPRASTARA
The process of Khandaprastara should also be made following the same rules of Akhandaprastara but observing some restrictions like devoid or containing a particular Anga. This is of two kinds and they are namely 1.Heenaprastara (Devoidpermutation), this is Angaheenaprastara in which the process of permutation should be made devoid of a particular Anga and 2.Yuktaprastara (Containingpermutation), this is like Ekangayuktaprastara, Dviyangayuktaprastara, Triangayuktaprastara and so on in which the process of permutation should be made containing a particular number of a particular Anga ( among them the word â€˜Angaâ€™ should be replaced with the name of an Anga among the six Talangas or â€˜Amshaâ€™ or unit like Anudrutaheenaprastara, Drutaheenaprastara of the respective Panchanga & Shadangaprastaras, Ekamshaheenaprastara, Dviamshaheenaprastara of Samyuktangaprastara of Heenaprastara, Ekanudrutayuktaprastara, Dvianudrutayuktaprastara, Tridrutayuktaprastara, Chaturlaghuyuktaprastara of the respective Panchanga & Shadangaprastaras and Ekaekamshayuktaprastara, Dviekamshayuktaprastara, Tridviamshayuktaprastara, Chaturchaturamshayuktaprastara of Samyuktangaprastara and so on of Yuktaprastara.
Example: If you carefully observe the 33 Akandaprastaras of 7DP you will find that Drutaheenaprastaras are â€˜0â€™, Ekadrutayuktaprastaras are â€˜12â€™, Tridrutayuktaprastaras are â€˜14â€™, Panchadrutayuktaprastaras are â€˜5â€™ and Saptadrutaprastara is â€˜1â€™ in Khandaprastara arriving at the total (12 + 14 + 6 + 1 =) 33. The same should be applied to all.
271012
0 Ś  01
0 l S  02
l 0 S  03
0 S l  04
0 l l l  05
l 0 l l  06
S 0 l  07
l l 0 l  08
Ś 0  09
l S 0 10
S l 0  11
l l l 0  12
271114
0 0 0 S  01
0 0 0 l l  02
0 0 l 0 l  03
0 l 0 0 l  04
l 0 0 0 l  05
0 0 S 0  06
0 0 l l 0  07
0 l 0 l 0  08
l 0 0 l 0  09
0 S 0 0  10
0 l l 0 0  11
l 0 l 0 0  12
S 0 0 0  13
l l 0 0 0  14
27156
0 0 0 0 0 l  01
0 0 0 0 l 0  02
0 0 0 l 0 0  03
0 0 l 0 0 0  04
0 l 0 0 0 0  05
l 0 0 0 0 0  06
27171
0 0 0 0 0 0 0  01
Like the â€˜Table of general permutationsâ€™ bringing out the details of Sankhya and Mahapatala of all the units of permutations of Akhandaprastara, in Khandaprastara, to bring out the details of the respective Sankhya and Mahapatala of Heenaprastara and Yuktaprastara of all respective Angas independent tables of each and every Anga have to be prepared. Thus, in Panchangaprastara, where five Angas are used in the process of permutation, an independent table to each of these five Angas have to be prepared, in Shadangaprastara, where six Angas are used in the process of permutation, six tables have to be prepared and in Samyuktangaprastara, depending upon the desired units of permutation, an independent table to each increasedunit should be prepared. For example please go through the item â€˜2.3.2.Khandaprastara and 2.4.Tables of angas and their applicationâ€™ in page 10 and the different tables of Druta, Laghu, Guru, Pluta and Kakapada of Panchangaprastara in Chapter3 of my book â€˜Indian genius in Talaprastaraâ€™. amsharma.
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#55
Dear member, sbala, Most of the month, February, 2007, I shall be on tour covering all the 12 Govt. Colleges of Music & Dance of Andhra Pradesh being my last visit. Whenever time and things permit I shall try to attend to your posts and reply. In the meantime try to finish off Khandaprastara also going through all the tables furnished in my book, â€˜Indian Genius in Talaprastaraâ€™. Wishing you all the best, amsharma.
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#56
Dear Msakella Sir,
I have given the details for the remaining permutations of 6DP Panchanga Nashta
1. (2619/6)
a. 196=13
b. 1310=3. 2nd proxy 6 undeducted. 1
c. 33=0 2nd proxy undeducted. 1
d. Remainder  2 O
e. 0011
2.(2619/8)
a. 198=11
b.1110=1. 2nd proxy 6 undeducted. 1
c. 1st proxy 3 undeducted. 0
d.1st proxy 2 undeducted. 0
e. 11=0 2nd proxy undeducted. 1
f. 1001
I will post the other permutations next. Please verify whenever you have time
I have given the details for the remaining permutations of 6DP Panchanga Nashta
1. (2619/6)
a. 196=13
b. 1310=3. 2nd proxy 6 undeducted. 1
c. 33=0 2nd proxy undeducted. 1
d. Remainder  2 O
e. 0011
2.(2619/8)
a. 198=11
b.1110=1. 2nd proxy 6 undeducted. 1
c. 1st proxy 3 undeducted. 0
d.1st proxy 2 undeducted. 0
e. 11=0 2nd proxy undeducted. 1
f. 1001
I will post the other permutations next. Please verify whenever you have time
Last edited by sbala on 04 Feb 2007, 11:33, edited 1 time in total.
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#57
(2619/9)
a. 199=10.
b. 1010=0 2nd proxy not deducted. 1
c. remainder  4 0
d. 00001
(2619/10)
a.1910=9
b.1st proxy 10 not deducted. 0
c.963=0. 4th proxy not deducted S
d. remainder  1 O
e. 0S0
(2619/11)
a.1911=8
b. 1st proxy 10 not deducted. O.
c. 86=2. 2nd proxy 3 not deducted. 1
d. 22=0 2nd proxy 2 not deducted. 1
e. Remainder  1 O
f. 0110
(2619/13)
a. 1913=6
b. 1st proxy 10 not deducted. O
c.66=0. 2nd proxy not deducted. 1
d. Remainder 3 O
e. 00010
(2619/14)
a. 1914=5
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d. 532=0. 4th proxy not deducted. S
e. S00
(2619/15)
a. 1915=4
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d.43=1 2nd proxy 2 not deducted. 1
e. 11=0 2nd proxy 1 not deducted 1
f. 1100
(2619/17)
a. 1917=2
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d. 1st proxy 3 not deducted. O
e. 22=0. 2nd proxy 1 not deducted. 1
f. remainder 1 0
g. 01000
(2619/18)
a. 1918=1
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d. 1st proxy 3 not deducted. O
e. 1st proxy 2 not deducted O
f. 11=0 2nd proxy not deducted 1
g. 10000
(2619/19)
a. 1919=0
b. remainder 6 O
c. 000000
a. 199=10.
b. 1010=0 2nd proxy not deducted. 1
c. remainder  4 0
d. 00001
(2619/10)
a.1910=9
b.1st proxy 10 not deducted. 0
c.963=0. 4th proxy not deducted S
d. remainder  1 O
e. 0S0
(2619/11)
a.1911=8
b. 1st proxy 10 not deducted. O.
c. 86=2. 2nd proxy 3 not deducted. 1
d. 22=0 2nd proxy 2 not deducted. 1
e. Remainder  1 O
f. 0110
(2619/13)
a. 1913=6
b. 1st proxy 10 not deducted. O
c.66=0. 2nd proxy not deducted. 1
d. Remainder 3 O
e. 00010
(2619/14)
a. 1914=5
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d. 532=0. 4th proxy not deducted. S
e. S00
(2619/15)
a. 1915=4
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d.43=1 2nd proxy 2 not deducted. 1
e. 11=0 2nd proxy 1 not deducted 1
f. 1100
(2619/17)
a. 1917=2
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d. 1st proxy 3 not deducted. O
e. 22=0. 2nd proxy 1 not deducted. 1
f. remainder 1 0
g. 01000
(2619/18)
a. 1918=1
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d. 1st proxy 3 not deducted. O
e. 1st proxy 2 not deducted O
f. 11=0 2nd proxy not deducted 1
g. 10000
(2619/19)
a. 1919=0
b. remainder 6 O
c. 000000
Last edited by sbala on 04 Feb 2007, 11:32, edited 1 time in total.
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#58
Dear member, sbala, Gone through your 56th & 57th posts and found correct. Your progress is very nice. Please apply this Nashta to all other Jaatis of Shadangaprastara also basing upon their respective proxies. After finishing this Akhandanashta you can proceed to Khandaprastara furnished by me in 54th & 55th posts and the instructions of them. From tomorrow onwards my trip to outstations starts and I shall get into touch with your posts whenever and wherever it becomes possible to me. Thinking of my absence donâ€™t neglect to do things. Wishing you all the best, amsharma.
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#59
Dear Msakella Sir,
I have given the Nashta for the first 6 permutations below. I will provide the remaining in subsequent posts. Please verify whenever you have time.
Shadanga Prastara Trisra Jathi 6ADP
(3625/1)
1. 251=24
2. 241374=0 6th proxy undedudcted
3. S
(3625/2)
1.252=23
2. 23137=3. 3rd proxy 4 undeducted. 1
3. 321=0 3rd proxy 1 undeducted 1
4. 11
(3625/3)
1. 253=22
2. 22137=2 3rd proxy 4 undeducted. 1
3. 22=0 2nd proxy undeducted O
4. 1 U remainder
5. U01
(3625/4)
1.254=21
2. 21137=1 3rd proxy 4 undeducted 1
3. 1st proxy 2 undeducted. U
4.11=0. 2nd proxy 1 undeducted O
5. 0U1
(3625/5)
1. 255=20
2. 20137=0 3rd proxy 4 undeducted 1
3. remainder 3 U
4. UUU1
(3625/6)
1.256=19
2. 1913=6 2nd proxy 7 undeducted O
3. 642=0 3rd proxy 1 undeducted 1
4. Remainder 1 U
4. U10
I have given the Nashta for the first 6 permutations below. I will provide the remaining in subsequent posts. Please verify whenever you have time.
Shadanga Prastara Trisra Jathi 6ADP
(3625/1)
1. 251=24
2. 241374=0 6th proxy undedudcted
3. S
(3625/2)
1.252=23
2. 23137=3. 3rd proxy 4 undeducted. 1
3. 321=0 3rd proxy 1 undeducted 1
4. 11
(3625/3)
1. 253=22
2. 22137=2 3rd proxy 4 undeducted. 1
3. 22=0 2nd proxy undeducted O
4. 1 U remainder
5. U01
(3625/4)
1.254=21
2. 21137=1 3rd proxy 4 undeducted 1
3. 1st proxy 2 undeducted. U
4.11=0. 2nd proxy 1 undeducted O
5. 0U1
(3625/5)
1. 255=20
2. 20137=0 3rd proxy 4 undeducted 1
3. remainder 3 U
4. UUU1
(3625/6)
1.256=19
2. 1913=6 2nd proxy 7 undeducted O
3. 642=0 3rd proxy 1 undeducted 1
4. Remainder 1 U
4. U10
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#61
Dear member, sbala, Last night I returned, saw your 59th & 60th posts and found correct. Very nice. Proceed further.
Again tomorrow I am leaving and return on 25th only again to leave on the same evening and to come back on 28th. From 1st March mostly I am free and regularly attend the posts of our forum. In the meantime try to finish the different kinds of Khandaprastara also. Wishing you all the best, amsharma.
Again tomorrow I am leaving and return on 25th only again to leave on the same evening and to come back on 28th. From 1st March mostly I am free and regularly attend the posts of our forum. In the meantime try to finish the different kinds of Khandaprastara also. Wishing you all the best, amsharma.
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#62
Dear msakella Sir,
I'm now reading your book and based on that I have given the anuloma prastara for 5DP. Please verify when you have time.
Pancanga Prastara (Akhanda)
Anuloma for 5DP
0S  01
011  02
101  03
0001  04
S0  05
110  06
0010  07
0100 08
1000 09
00000 10
I'm now reading your book and based on that I have given the anuloma prastara for 5DP. Please verify when you have time.
Pancanga Prastara (Akhanda)
Anuloma for 5DP
0S  01
011  02
101  03
0001  04
S0  05
110  06
0010  07
0100 08
1000 09
00000 10
Last edited by sbala on 25 Feb 2007, 16:56, edited 1 time in total.
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 Posts: 29
 Joined: 01 Oct 2006, 15:27
#66
Sbala,
I know,since i learn from him..........i am also learning Talaprastara.But i got stuck midway midway due to my mother's illness and since then i havent really gone back to it. But i am amazed at your speed and that too since you are learning on the net. You have inspired me!!!!!!!!!!!
I know,since i learn from him..........i am also learning Talaprastara.But i got stuck midway midway due to my mother's illness and since then i havent really gone back to it. But i am amazed at your speed and that too since you are learning on the net. You have inspired me!!!!!!!!!!!
Last edited by sandhyashree on 28 Feb 2007, 21:55, edited 1 time in total.
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#68
Sandhya  Good to know I'm inspiring someone. But, I prefer to lie low till I understand this completely. Why don't you share your experiences learning with Sharmaji and other subjects you have learnt from him? I know he has done lot of work on teaching methods for kalpanaswaras and raga alaapanais
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#69
kji,
I dont know if you have been poked in your waist my mamis asking you to name the raga during concerts. I have had to endure the interrogation, my waistline has reduced and I'm yet to open the scoreboard in the "mami's quiz".
I dont know if you have been poked in your waist my mamis asking you to name the raga during concerts. I have had to endure the interrogation, my waistline has reduced and I'm yet to open the scoreboard in the "mami's quiz".
Last edited by sbala on 16 Mar 2007, 13:06, edited 1 time in total.
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#70
Sbala,
Yes, definitely........
You can shoot an email to [email protected] since it might mean a deviation from the topic here....
i'll be more than glad to share my learning experiences with you........
Yes, definitely........
You can shoot an email to [email protected] since it might mean a deviation from the topic here....
i'll be more than glad to share my learning experiences with you........
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#71
Dear Sharmaji,
Please check the details of Viloma Prastara. What is the significance of Viloma apart from it just being the opposite of anuloma? I have heard his terms being used in the context of pallavis.
Akhanda Viloma Prastara for 6DP
000000 01
10000 02
01000 03
00100 04
1100 05
S00 06
00010 07
1010 08
0110 09
0S0 10
00001 11
1001 12
0101 13
0011 14
111 15
S1 16
00S 17
1S 18
Ś 19
Please check the details of Viloma Prastara. What is the significance of Viloma apart from it just being the opposite of anuloma? I have heard his terms being used in the context of pallavis.
Akhanda Viloma Prastara for 6DP
000000 01
10000 02
01000 03
00100 04
1100 05
S00 06
00010 07
1010 08
0110 09
0S0 10
00001 11
1001 12
0101 13
0011 14
111 15
S1 16
00S 17
1S 18
Ś 19
Last edited by sbala on 10 Mar 2007, 13:05, edited 1 time in total.
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#74
Dear member, sbala, Your Akhandavilomaprastara is OK.
While writing the figures in obverse order is natural and necessary writing them in reverse order also is just another variety to make all of us more acquainted with them. In our younger days our parents are used to make all of us recite the mathematical tables both in obverse and reverse orders just to give more acquaintance with them. In the same manner this Vilomaprastara also helps to give us more acquaintance with the process of permutation. In fact, this was first mentioned in â€˜Nartananirnayaâ€™ of Pandarika Vithala of 16th century in the name of Vipareetaprastara. But, to make the names of both obverse and reverse patterns of prastara, I have myself coined these names of Anulomaprastara and Vilomaprastara. In our Indian Culture the obverse and reverse orders are called Anuloma and Viloma respectively and these names are appended to the things which have used these orders and in the same manner in our music also this has been utilized.
Your progress is excellent. Keep it up. But, a small correction. In 271112 the permutation â€˜Sâ€™0â€™ becomes the 9th but not 11th. Please note. Mostly you have got good acquaintance with the process of permutation and you need to maintain this level of acquaintance by attending to it regularly tallying their Sankhya with the relevant tables. Now, try to concentrate much upon Khandanashta, uddishta and kalita basing upon the respective rules and regulations furnished in the book. Proceed and write postings for clarification. I hope you will definitely be able to get through with them also. Wishing you all the best, amsharma.
While writing the figures in obverse order is natural and necessary writing them in reverse order also is just another variety to make all of us more acquainted with them. In our younger days our parents are used to make all of us recite the mathematical tables both in obverse and reverse orders just to give more acquaintance with them. In the same manner this Vilomaprastara also helps to give us more acquaintance with the process of permutation. In fact, this was first mentioned in â€˜Nartananirnayaâ€™ of Pandarika Vithala of 16th century in the name of Vipareetaprastara. But, to make the names of both obverse and reverse patterns of prastara, I have myself coined these names of Anulomaprastara and Vilomaprastara. In our Indian Culture the obverse and reverse orders are called Anuloma and Viloma respectively and these names are appended to the things which have used these orders and in the same manner in our music also this has been utilized.
Your progress is excellent. Keep it up. But, a small correction. In 271112 the permutation â€˜Sâ€™0â€™ becomes the 9th but not 11th. Please note. Mostly you have got good acquaintance with the process of permutation and you need to maintain this level of acquaintance by attending to it regularly tallying their Sankhya with the relevant tables. Now, try to concentrate much upon Khandanashta, uddishta and kalita basing upon the respective rules and regulations furnished in the book. Proceed and write postings for clarification. I hope you will definitely be able to get through with them also. Wishing you all the best, amsharma.
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