# Ticket #7712(closed defect: duplicate)

Opened 3 years ago

## error with polynomial with interval coefficients

Reported by: Owned by: zimmerma AlexGhitza major sage-duplicate/invalid/wontfix basic arithmetic kohel N/A Travis Scrimshaw #13760

Consider the following example:

```sage: P.<y,z> = PolynomialRing(RealIntervalField(2))
sage: Q.<x> = PolynomialRing(P)
sage: C = (y-x)^3
sage: C(y/2)
0
```

I do not understand why the result is 0. In fact there are two errors: (i) the result is a polynomial of degree 3 in y, thus y3 should appear (ii) the result should "contain" the exact result which is 0.125*y3, thus it should be c*y3 where c is an interval containing 0.125. Compare the following with a precision of 10 bits:

```sage: P.<y,z> = PolynomialRing(RealIntervalField(10))
sage: Q.<x> = PolynomialRing(P)
sage: C = (y-x)^3
sage: C(y/2)
0.12500?*y^3
```

## Change History

### comment:1 Changed 3 years ago by ylchapuy

It seems it just a printing issue:

```sage: r = C(y/2)
sage: r
0
sage: r.monomials()
[y^3]
sage: r.monomial_coefficient(y^3).str(style='brackets')
'[-0.00 .. 0.25]'
```

### comment:2 Changed 3 years ago by zimmerma

• Summary changed from error in polynomial substitution with interval coefficients to error in printing interval coefficients (together with variables)

Indeed:

```sage: R=RealIntervalField(2)
sage: r=R(-0.00,0.25)
sage: r.str(style='brackets')
'[-0.00 .. 0.25]'
sage: r
1.?
sage: r*x
0
```

I thus changed the summary.

### comment:3 follow-up: ↓ 6 Changed 3 years ago by zimmerma

• Summary changed from error in printing interval coefficients (together with variables) to error with polynomial with interval coefficients

Here is a more complex example, which shows this is not only a printing issue:

```def method2(prec):
n=[0,9,7,8,11,6,3,7,6,6,4,3,4,1,2,2,1,1,1,2,0,0,0,3,0,0,0,0,1]
R = RealIntervalField(prec)
P.<xk1,sk1,sk2> = PolynomialRing(R)
Q.<xk> = PolynomialRing(P)
C = (sk1-xk)^n[1]*xk^n[2]
C=C.integral()
C=C(sk1/2)-C(xk1)
C=R(10^6)*C.subs(sk1=sk2-xk1)
C=C.subs(xk1=xk,sk2=sk1)
for k in range(3,29):
C=C*xk^n[k]
C=C.integral()
C=C(sk1/k)-C(xk1)
C=R(10^6)*C.subs(sk1=sk2-xk1)
C=C.subs(xk1=xk,sk2=sk1)
C=C.subs(xk=R(0),sk1=R(1))
return C(0,0,0)

sage: method2(391)
0
sage: _.parent()
Integer Ring

sage: method2(392)
1.?e-8
sage: _.parent()
Real Interval Field with 392 bits of precision
```

Normally, both calls should return an object of type "Real Interval Field", isn't it? (If necessary, I can open a different trac ticket for both issues.)

### comment:4 Changed 3 years ago by was

• Milestone changed from sage-4.3 to sage-4.3.1

I'm declaring a total feature freeze on sage-4.3.

### comment:5 Changed 3 years ago by zimmerma

Still there in 4.3.1.

### comment:6 in reply to: ↑ 3 Changed 3 years ago by ylchapuy

• Summary changed from error with polynomial with interval coefficients to _

C=C.subs(xk=R(0),sk1=R(1))

The two polynomials obtained here are constants. The strange behaviour about the type comes from line 153 of

sage/rings/polynomial/multi_polynomial_element.py

where we find:

```        try:
K = x[0].parent()     <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
except AttributeError:
K = self.parent().base_ring()
y = K(0)
for (m,c) in self.element().dict().iteritems():
y += c*misc.mul([ x[i]**m[i] for i in range(n) if m[i] != 0])
```

I don't know exactly why, but It first try to take the type of the first input (here Integer 0) and this type is then changed only by coercion when doing the computation.

With precision 391 the polynomial is null and no operations are performed, so the results stays Integer.

I would say this is a bug but maybe there is a purpose behind this.

### comment:7 Changed 3 years ago by ylchapuy

• Summary changed from _ to error with polynomial with interval coefficients

### comment:8 follow-up: ↓ 9 Changed 3 years ago by zimmerma

Yann, are you sure this method call is called? I've added a print statement before y=K(0) and nothing is printed (in 4.3.3). I add David in cc, maybe he can help us.

### comment:9 in reply to: ↑ 8 Changed 3 years ago by ylchapuy

Sorry, my last comment was not clear. The method call is called when you do return C(0,0,0).

### comment:10 Changed 3 years ago by zimmerma

Sorry, my last comment was not clear. The method call is called when you do return C(0,0,0).

with C(0,0,0) I see no problem:

```sage: P.<y,z> = PolynomialRing(RealIntervalField(2))
sage: Q.<x> = PolynomialRing(P)
sage: C = (y-x)^3
sage: a=C(0,0,0)
sage: type(a)
<type 'sage.rings.real_mpfi.RealIntervalFieldElement'>
sage: a.lower()
0.00
sage: a.upper()
0.00
```

### comment:11 Changed 3 years ago by ylchapuy

Here is my point:

```sage: def method2(prec):
....:        n=[0,9,7,8,11,6,3,7,6,6,4,3,4,1,2,2,1,1,1,2,0,0,0,3,0,0,0,0,1]
....:    R = RealIntervalField(prec)
....:    P.<xk1,sk1,sk2> = PolynomialRing(R)
....:    Q.<xk> = PolynomialRing(P)
....:    C = (sk1-xk)^n[1]*xk^n[2]
....:    C=C.integral()
....:    C=C(sk1/2)-C(xk1)
....:    C=R(10^6)*C.subs(sk1=sk2-xk1)
....:    C=C.subs(xk1=xk,sk2=sk1)
....:    for k in range(3,29):
....:           C=C*xk^n[k]
....:       C=C.integral()
....:       C=C(sk1/k)-C(xk1)
....:       C=R(10^6)*C.subs(sk1=sk2-xk1)
....:       C=C.subs(xk1=xk,sk2=sk1)
....:    C=C.subs(xk=R(0),sk1=R(1))
....:    return C
....:
sage: C391 = method2(391)
sage: C391
0
sage: type(C391)
<class 'sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict'>
sage: type(C391(0,0,0))
<type 'sage.rings.integer.Integer'>
sage: type(C391(GF(17)['z'](0),0,0))
<type 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'>
```

### comment:12 Changed 3 years ago by zimmerma

Here is my point: [...]

ok, I thought you were speaking about the first (smaller) examples. I can reduce this second problem to the following:

```sage: R.<x,y> = PolynomialRing(RR)
sage: f=R(1); type(f(0,0))
<type 'sage.rings.real_mpfr.RealNumber'>
sage: f=R(0); type(f(0,0))
<type 'sage.rings.integer.Integer'>
```

David, please can you explain why it is so?

### comment:13 Changed 6 months ago by gmoroz

I didn't see this ticket when submitting the new ticket #13760. There I provide a patch that corrects this bug. The two tickets should be merged (and probably closed after review of the patch).

### Changed 5 months ago by gmoroz

Tests should work after applying trac 13760 patch

### comment:14 Changed 5 months ago by zimmerma

• Description modified (diff)

### comment:15 Changed 5 months ago by gmoroz

• Status changed from new to needs_review

### comment:16 Changed 5 months ago by zimmerma

• Dependencies set to #13760

I propose to mark this as "duplicate", since #13760 solves that issue.

Paul

### comment:17 Changed 5 months ago by tscrim

• Status changed from needs_review to positive_review
• Reviewers set to Travis Scrimshaw
• Milestone changed from sage-5.6 to sage-duplicate/invalid/wontfix

Hey Paul and Guillaume,

For future reference, just mark the patch as duplicate in the milestone dropdown and set it to needs_review.

#13760 does seem to fix the problem:

```sage: method2(391)
0.?e-8
sage: _.parent()
Real Interval Field with 391 bits of precision
```

Best,
Travis

### comment:18 Changed 5 months ago by jdemeyer

• Status changed from positive_review to closed
• Resolution set to duplicate
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