## Bug #1101

### Bug in MinPolyModular (insufficient rational reconstruction)

Status:

Closed

Priority:

High

Assignee:

Category:

Buggy Maths

Target version:

**Description**

Rational reconstruction succeeds "too early"

/**/ L:=[3*x^3*y +3*y*z^3 +1, 2*x*y*z^2 +3*x, 2*y^3*z +1]; /**/ I := ideal(L); /**/ mp := MinPolyQuot(x, I, x); /**/ mp isin I; false /**/ mp; x^16 +(15/2)*x^10 +(45/4)*x^4 +(-1/2028)*x

**Related issues**

### History

#### #1 Updated by Anna Maria Bigatti 10 months ago

**Project**changed from*CoCoA-5*to*CoCoALib***Category**changed from*enhancing/improving*to*Buggy Maths***Target version**changed from*CoCoA-5.2.2*to*CoCoALib-0.99560***% Done**changed from*0*to*20*

Adding Horner evaluation to check minpoly correct reconstruction.

#### #2 Updated by Anna Maria Bigatti 10 months ago

**Related to***Bug #1100: PrimaryDecomposition0: says not 0-dim but IsZeroDim says ideal is zero-dim!*added

#### #3 Updated by Anna Maria Bigatti 10 months ago

**Status**changed from*New*to*Resolved***Priority**changed from*Normal*to*High***% Done**changed from*20*to*70***Estimated time**set to*3.00 h*

Fixed. I implemented a Horner evaluation in `MinPoly.C`

which may be improved, and maybe moved into some other file (and also exported to cocoa5, so we can delete it from `PrimaryDecomposition0.cpkg5`

).

/**/ L:=[3*x^3*y +3*y*z^3 +1, 2*x*y*z^2 +3*x, 2*y^3*z +1]; /**/ I := ideal(L); /**/ mp := MinPolyQuot(x, I, x); /**/ mp isin I; /**/ /**/ /**/ true /**/ mp; x^16 +(15/2)*x^10 +(45/4)*x^4 +(1594195/5184)*x

#### #4 Updated by John Abbott 10 months ago

Here are some more examples which the computer found during the night:

[3*x*y*z^3 +z^2 +1, 3*y^3*z +z^2, 2*x*y^2*z^2 +3*x*y*z^2] [x^2*y^2 +3*y^3*z +1, x*y*z^2 +x*y^2, 2*y^3 +3]

#### #5 Updated by John Abbott 10 months ago

JAA has added `test-MinPoly1.C`

including the 3 examples listed here.

Checking in now.

#### #6 Updated by John Abbott 8 months ago

**Status**changed from*Resolved*to*Feedback***% Done**changed from*70*to*90*

#### #7 Updated by John Abbott 7 months ago

**Status**changed from*Feedback*to*Closed***% Done**changed from*90*to*100*

#### #8 Updated by Anna Maria Bigatti 4 months ago

**Related to***Slug #1165: MinPoly over QQ: verification may be very slow*added