SymbolicPolynomialMod
- To: mathgroup at smc.vnet.net
- Subject: [mg106564] SymbolicPolynomialMod
- From: Artur <grafix at csl.pl>
- Date: Sat, 16 Jan 2010 06:13:13 -0500 (EST)
- References: <201001141046.FAA19729@smc.vnet.net> <201001150817.DAA29607@smc.vnet.net> <4B509BB1.5050803@csl.pl> <4B50B86E.5000800@wolfram.com>
- Reply-to: grafix at csl.pl
Dear Mathematica Gurus!
Who know how to execute SymbolicPolynomialMod
PolynomialMod working only on numbers (not for symbols)
If we know that a,b,c,d,f are five roots of general quintic polynomial
X^5+t X^4+p X^3+q X^2+r X+s==0
Then we can do SymbolicPolynomialMod of g (manually not by Mathemathica
unfortunatelly)
g=(a^6 b^7 c^5 d^2 + a^7 b^5 c^6 d^2 + a^5 b^6 c^7 d^2 +
a^7 b^6 c^2 d^5 + a^2 b^7 c^6 d^5 + a^6 b^2 c^7 d^5 +
a^5 b^7 c^2 d^6 + a^7 b^2 c^5 d^6 + a^2 b^5 c^7 d^6 +
a^6 b^5 c^2 d^7 + a^2 b^6 c^5 d^7 + a^5 b^2 c^6 d^7 -
a^6 b^8 c^3 d^2 f - a^8 b^3 c^6 d^2 f - a^3 b^6 c^8 d^2 f -
a^8 b^6 c^2 d^3 f - a^2 b^8 c^6 d^3 f - a^6 b^2 c^8 d^3 f -
a^3 b^8 c^2 d^6 f - a^8 b^2 c^3 d^6 f - a^2 b^3 c^8 d^6 f -
a^6 b^3 c^2 d^8 f - a^2 b^6 c^3 d^8 f - a^3 b^2 c^6 d^8 f +
a^7 b^6 c^5 f^2 + a^5 b^7 c^6 f^2 + a^6 b^5 c^7 f^2 -
a^8 b^6 c^3 d f^2 - a^3 b^8 c^6 d f^2 - a^6 b^3 c^8 d f^2 -
a^6 b^8 c d^3 f^2 - a^8 b c^6 d^3 f^2 - a b^6 c^8 d^3 f^2 +
a^6 b^7 d^5 f^2 + a^7 c^6 d^5 f^2 + b^6 c^7 d^5 f^2 +
a^7 b^5 d^6 f^2 - a^8 b^3 c d^6 f^2 - a b^8 c^3 d^6 f^2 +
b^7 c^5 d^6 f^2 + a^5 c^7 d^6 f^2 - a^3 b c^8 d^6 f^2 +
a^5 b^6 d^7 f^2 + a^6 c^5 d^7 f^2 + b^5 c^6 d^7 f^2 -
a^3 b^6 c d^8 f^2 - a^6 b c^3 d^8 f^2 - a b^3 c^6 d^8 f^2 -
a^6 b^8 c^2 d f^3 - a^8 b^2 c^6 d f^3 - a^2 b^6 c^8 d f^3 -
a^8 b^6 c d^2 f^3 - a b^8 c^6 d^2 f^3 - a^6 b c^8 d^2 f^3 -
a^2 b^8 c d^6 f^3 - a^8 b c^2 d^6 f^3 - a b^2 c^8 d^6 f^3 -
a^6 b^2 c d^8 f^3 - a b^6 c^2 d^8 f^3 - a^2 b c^6 d^8 f^3 +
a^6 b^7 c^2 f^5 + a^7 b^2 c^6 f^5 + a^2 b^6 c^7 f^5 +
a^7 b^6 d^2 f^5 + b^7 c^6 d^2 f^5 + a^6 c^7 d^2 f^5 +
a^2 b^7 d^6 f^5 + a^7 c^2 d^6 f^5 + b^2 c^7 d^6 f^5 +
a^6 b^2 d^7 f^5 + b^6 c^2 d^7 f^5 + a^2 c^6 d^7 f^5 +
a^7 b^5 c^2 f^6 + a^2 b^7 c^5 f^6 + a^5 b^2 c^7 f^6 -
a^8 b^3 c^2 d f^6 - a^2 b^8 c^3 d f^6 - a^3 b^2 c^8 d f^6 +
a^5 b^7 d^2 f^6 - a^3 b^8 c d^2 f^6 - a^8 b c^3 d^2 f^6 +
a^7 c^5 d^2 f^6 + b^5 c^7 d^2 f^6 - a b^3 c^8 d^2 f^6 -
a^8 b^2 c d^3 f^6 - a b^8 c^2 d^3 f^6 - a^2 b c^8 d^3 f^6 +
a^7 b^2 d^5 f^6 + b^7 c^2 d^5 f^6 + a^2 c^7 d^5 f^6 +
a^2 b^5 d^7 f^6 + a^5 c^2 d^7 f^6 + b^2 c^5 d^7 f^6 -
a^2 b^3 c d^8 f^6 - a^3 b c^2 d^8 f^6 - a b^2 c^3 d^8 f^6 +
a^5 b^6 c^2 f^7 + a^6 b^2 c^5 f^7 + a^2 b^5 c^6 f^7 +
a^6 b^5 d^2 f^7 + b^6 c^5 d^2 f^7 + a^5 c^6 d^2 f^7 +
a^2 b^6 d^5 f^7 + a^6 c^2 d^5 f^7 + b^2 c^6 d^5 f^7 +
a^5 b^2 d^6 f^7 + b^5 c^2 d^6 f^7 + a^2 c^5 d^6 f^7 -
a^3 b^6 c^2 d f^8 - a^6 b^2 c^3 d f^8 - a^2 b^3 c^6 d f^8 -
a^6 b^3 c d^2 f^8 - a b^6 c^3 d^2 f^8 - a^3 b c^6 d^2 f^8 -
a^2 b^6 c d^3 f^8 - a^6 b c^2 d^3 f^8 - a b^2 c^6 d^3 f^8 -
a^3 b^2 c d^6 f^8 - a b^3 c^2 d^6 f^8 - a^2 b c^3 d^6 f^8)
by substitutions g/. {a^5->-t a^4-p a^3-q a^2-r a-s,b^5->-t b^4-p b^3-q
b^2-r b-s,
c^5->-t c^4-p c^3-q c^2-r c-s,d^5->-t d^4-p d^3-q d^2-r d-s,f^5->-t
f^4-p f^3-q f^2-r f-s}
etc.
How we can do full SymbolicPolynomialMod on the form g after such
procedure will be not higher degree as 4 for a,b,c,d,f ?
Best wishes
Artur
- References:
- Trouble with coupled quadratic equations where the solutions are degenerate/symmetric
- From: Robert Hoy <robert.hoy@yale.edu>
- Re: Trouble with coupled quadratic equations where the
- From: Daniel Lichtblau <danl@wolfram.com>
- Trouble with coupled quadratic equations where the solutions are degenerate/symmetric