# Revision history [back]

### How to determine the coefficients of a polynomial when they depend on variables?

Suppose that EXP2 is a polynomial expression in the variables X_1,X_2,...,X_n with coefficients that depend on the variables B_1,B_2,...,B_n. Suppose EXP1 is an expression equal to EXP2, but scrambled.

Given EXP1, how can I automatically obtain EXP2?

For example, if I have

a=var('a') b=var('b') c=var('c') d=var('d') e=var('e') eqn=a==bd^2+ce^2+e(b+2c*d),

how can I automatically rewrite a as a polynomial in b and c, so that I get an equation that looks like

a==b(d^2+e)+c(e^2+2ed)?

### How to determine the coefficients of a polynomial when they depend on variables?

Suppose that EXP2 is a polynomial expression in the variables X_1,X_2,...,X_n with coefficients that depend on the variables B_1,B_2,...,B_n. Suppose EXP1 is an expression equal to EXP2, but scrambled.

Given EXP1, how can I automatically obtain EXP2?

For example, if I have

[code] a=var('a') b=var('b') c=var('c') d=var('d') e=var('e') eqn=a==bd^2+ce^2+e(b+2c*d),c*d), [\code]

how can I automatically rewrite a as a polynomial in b and c, so that I get an equation that looks like

a==b(d^2+e)+c(e^2+2ed)?

### How to determine the coefficients of a polynomial when they depend on variables?

Suppose that EXP2 is a polynomial expression in the variables X_1,X_2,...,X_n with coefficients that depend on the variables B_1,B_2,...,B_n. Suppose EXP1 is an expression equal to EXP2, but scrambled.

Given EXP1, how can I automatically obtain EXP2?

For example, if I have

[code] a=var('a') b=var('b') c=var('c') d=var('d') e=var('e') a=var('a')

b=var('b')

c=var('c')

d=var('d')

e=var('e')

eqn=a==bd^2+ce^2+e(b+2c*d), [\code]c*d),

how can I automatically rewrite a as a polynomial in b and c, so that I get an equation that looks like

a==b(d^2+e)+c(e^2+2ed)?

### How to determine the coefficients of a polynomial when they depend on variables?

Suppose that EXP2 is a polynomial expression in the variables X_1,X_2,...,X_n with coefficients that depend on the variables B_1,B_2,...,B_n. Suppose EXP1 is an expression equal to EXP2, but scrambled.

Given EXP1, how can I automatically obtain EXP2?

For example, if I have

a=var('a')

b=var('b')

c=var('c')

d=var('d')

e=var('e')

eqn=a==bd^2+ce^2+e(b+2c*d),

how can I automatically rewrite a as a polynomial in b and c, so that I get an equation that looks like

a==b(d^2+e)+c(e^2+2ed)?

### How to determine the coefficients of a polynomial when they depend on variables?

Suppose that EXP2 is a polynomial expression in the variables X_1,X_2,...,X_n with coefficients that depend on the variables B_1,B_2,...,B_n. B_1,B_2,...,B_m. Suppose EXP1 is an expression equal to EXP2, but scrambled.

Given EXP1, how can I automatically obtain EXP2?

For example, if I have

a=var('a')

b=var('b')

c=var('c')

d=var('d')

e=var('e')

eqn=a==bd^2+ce^2+e(b+2c*d),

how can I automatically rewrite a as a polynomial in b and c, so that I get an equation that looks like

a==b(d^2+e)+c(e^2+2ed)?