# Polynomial command

Hello How can I write a polynomial such as f(x^2-4,x^2-2*x) in sage?

Polynomial command

Hello How can I write a polynomial such as f(x^2-4,x^2-2*x) in sage?

1

Not sure what `x^y^2`

was supposed to be in your polynomial `f`

.
Anyway, try something like this.

```
sage: R.<x,y> = PolynomialRing(ZZ, order='deglex')
sage: f = x^5 * y^2 + x^3 * y^2 - y + 1
sage: F = (x * y^2 - x, x - y^3)
sage: f.reduce(F)
x^5 + x^3 - y + 1
```

Asked: **
2013-04-04 01:12:47 -0600
**

Seen: **178 times**

Last updated: **Apr 15 '13**

how to sum up the function over all permutations of variables in associative non-commutative algebra

how to check algebraic equations?

substitution of ideal generators of a free algebra

How to reorder terms in an expression to follow a specific order?

equation does not simplify due to fractional exponent

Very basic simplification question

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.

What do you mean ? You have a polynomial of two variables and you want to substitute a polynomial in x for each variable ?

I have a polynomial f= x^*y^2+x^3*y^2-y+1 and I want to compute the remainder on division of the given polynomial f by the order set F using grlex order ,but F is F=(x*y^2-x,x-y^3) that has two part, I don't know how to introduce F in sage for division algorithm.