Revision history [back]

I'm trying to use symbolic ring as a media for conversion between complex algebraic entities. However, I've encountered an issue when the substitution does not quite work. The following code illustrates the issue, where only part of the variables are substituted. Namely, symbolic variables x and t remain intact despite of the request to substitute them with xx and tt:

R = PolynomialRing(QQ,2,'s')
s = R.gens()
K.<x,t> = R[[]]
f = (s[0]+s[1])*x + (s[0]^2+s[1]^2)*x^2 + t*x^3
fs = SR( f.polynomial() )
print(f'fs: {fs.parent()} {fs.variables()}')

var('ss0','ss1','xx','tt')
fn = fs.subs({SR(s[0]):ss0, SR(s[1]):ss1, SR(t):tt, SR(x):xx})
print(f'fn: {fn.parent()} {fn.variables()}')

The output is

fs: Symbolic Ring (s0, s1, t, x)
fn: Symbolic Ring (ss0, ss1, t, x)

What's wrong?

I'm trying to use symbolic ring as a media for conversion between complex algebraic entities. However, I've encountered an issue when the substitution does not quite work. The following code illustrates the issue, where only part of the variables are substituted. Namely, symbolic variables x and t remain intact despite of the request to substitute them with xx and tt:

R = PolynomialRing(QQ,2,'s')
s = R.gens()
K.<x,t> = R[[]]
f = (s[0]+s[1])*x + (s[0]^2+s[1]^2)*x^2 + t*x^3
fs = SR( f.polynomial() )
print(f'fs: {fs.parent()} {fs.variables()}')

var('ss0','ss1','xx','tt')
fn = fs.subs({SR(s[0]):ss0, SR(s[1]):ss1, SR(t):tt, SR(x):xx})
print(f'fn: {fn.parent()} {fn.variables()}')

The output is

fs: Symbolic Ring (s0, s1, t, x)
fn: Symbolic Ring (ss0, ss1, t, x)

What's wrong?

fn = fs.subs({SR(s[0]):ss0, SR(s[1]):ss1, SR(t.polynomial()):tt, SR(x.polynomial()):xx})

I'm trying to use symbolic ring as a media for conversion between complex algebraic entities. However, I've encountered an issue when the substitution does not quite work. The following code illustrates the issue, where only part of the variables are substituted. Namely, symbolic variables x and t remain intact despite of the request to substitute them with xx and tt:

R = PolynomialRing(QQ,2,'s')
s = R.gens()
K.<x,t> = R[[]]
f = (s[0]+s[1])*x + (s[0]^2+s[1]^2)*x^2 + t*x^3
fs = SR( f.polynomial() )
print(f'fs: {fs.parent()} {fs.variables()}')

var('ss0','ss1','xx','tt')
fn = fs.subs({SR(s[0]):ss0, SR(s[1]):ss1, SR(t):tt, SR(x):xx})
print(f'fn: {fn.parent()} {fn.variables()}')

The output is

fs: Symbolic Ring (s0, s1, t, x)
fn: Symbolic Ring (ss0, ss1, t, x)

What's wrong?

UPDATE. Apparently, the substitution

fn = fs.subs({SR(s[0]):ss0, SR(s[1]):ss1, SR(t.polynomial()):tt, SR(x.polynomial()):xx})

works as expected. So, it seems that Sage does not recognize SR(t) and SR(t.polynomial()) as the same variable. Is this expected?

I'm trying to use symbolic ring as a media for conversion between complex algebraic entities. However, I've encountered an issue when the substitution does not quite work. The following code illustrates the issue, where only part of the variables are substituted. Namely, symbolic variables x and t remain intact despite of the request to substitute them with xx and tt:

R = PolynomialRing(QQ,2,'s')
s = R.gens()
K.<x,t> = R[[]]
f = (s[0]+s[1])*x + (s[0]^2+s[1]^2)*x^2 + t*x^3
fs = SR( f.polynomial() )
print(f'fs: {fs.parent()} {fs.variables()}')

var('ss0','ss1','xx','tt')
fn = fs.subs({SR(s[0]):ss0, SR(s[1]):ss1, SR(t):tt, SR(x):xx})
print(f'fn: {fn.parent()} {fn.variables()}')

The output is

fs: Symbolic Ring (s0, s1, t, x)
fn: Symbolic Ring (ss0, ss1, t, x)

What's wrong?

UPDATE. Apparently, the substitution

fn = fs.subs({SR(s[0]):ss0, SR(s[1]):ss1, SR(t.polynomial()):tt, SR(x.polynomial()):xx})

works as expected. So, it seems that Sage does not recognize SR(t) and SR(t.polynomial()) as the same variable. Is this expected?

I'm trying to use symbolic ring as a media for conversion between complex algebraic entities. However, I've encountered an issue when the substitution does not quite work. The following code illustrates the issue, where only part of the variables are substituted. Namely, symbolic variables x and t remain intact despite of the request to substitute them with xx and tt:

R = PolynomialRing(QQ,2,'s')
s = R.gens()
K.<x,t> = R[[]]
f = (s[0]+s[1])*x + (s[0]^2+s[1]^2)*x^2 + t*x^3
fs = SR( f.polynomial() )
print(f'fs: {fs.parent()} {fs.variables()}')

var('ss0','ss1','xx','tt')
fn = fs.subs({SR(s[0]):ss0, SR(s[1]):ss1, SR(t):tt, SR(x):xx})
print(f'fn: {fn.parent()} {fn.variables()}')

The output is

fs: Symbolic Ring (s0, s1, t, x)
fn: Symbolic Ring (ss0, ss1, t, x)

What's wrong?

UPDATE. Apparently, the substitution

fn = fs.subs({SR(s[0]):ss0, SR(s[1]):ss1, SR(t.polynomial()):tt, SR(x.polynomial()):xx})

works as expected. So, it seems that Sage does not recognize SR(t) and SR(t.polynomial()) as the same variable. Is this expected?