[sage-support] Re: Test if p(x) is in a ring generated by polynomials

2010-09-14 Thread James Parson
On Sep 8, 2:57 am, Cary Cherng cche...@gmail.com wrote: I am not familiar with algebraic geometry or its terminology and new to sage. p_1,...p_n and q are elements of Z[x_1,...,x_n]. In my context I have some evidence that q can be written as something like q = p_1*p_2 + ... + p_5*p_6. In

Re: [sage-support] Re: Test if p(x) is in a ring generated by polynomials

2010-09-12 Thread Mitesh Patel
On 09/11/2010 11:30 PM, john_perry_usm wrote: I would try this: 1. Let M be an augmented matrix over the *integer* ring whose entries in the left block are (as you state) the coefficients of p_1*p_2, ... p_i*p_j. You can create a matrix over the integer ring using M = matrix(ZZ,...). 2.

[sage-support] Re: Test if p(x) is in a ring generated by polynomials

2010-09-11 Thread john_perry_usm
I would try this: 1. Let M be an augmented matrix over the *integer* ring whose entries in the left block are (as you state) the coefficients of p_1*p_2, ... p_i*p_j. You can create a matrix over the integer ring using M = matrix(ZZ,...). 2. Echelonize the matrix: M.echelonize(). 3. See if you

[sage-support] Re: Test if p(x) is in a ring generated by polynomials

2010-09-09 Thread Cary Cherng
Suppose I form the row matrix: M = [ (p_1*p_2, .., p_i*p_j) ] and then try looking for a column vector x satifying M*x = q where the elements of x are integers, hopefully 1 or -1. If I tried this approach how would I get sage to only consider integer vectors x as solutions. On Sep 8, 6:20 am,

[sage-support] Re: Test if p(x) is in a ring generated by polynomials

2010-09-08 Thread john_perry_usm
Are you asking whether q=p_1*p_2+...+p_5*p_6? If so, you can simply construct q and the p_i, then test for equality: sage: q == p_1*p_2 + ... + p_5*p_6 True (or False, depending) (you would fill in the ellipsis with the form you want, which is not obvious to me from what you've written). If