I got linear zero dimensional ideal in 48 variables over QQ and when I
run .variety() I get error and traceback. Looks like the python
exception isn't caught due to a deeper error. Groebner basis of the
ideal works.
For most ideals, variety works.
Tested on 10.6 on linux
>From the attached testcase:
print("dimension=",Ideal(J).dimension()) # returns 0
try:
va=Ideal(J).variety()
print(" variety passed")
except Exception as e:
print(" exception in variety ",e) #error skipping text from `)`
error at token `)` and traceback
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"""
Bug in variety of zero dimenstional ideal
Author: Georgi Guninski 2025-05-20
"""
Kx=PolynomialRing(QQ,'x',48)
Kx.inject_variables()
J=[2*x0 + 3*x1 + 5*x2 + 7*x3 + 11*x4 + 13*x5 + 17*x6 + 19*x7, 2*x8 + 3*x9 +
5*x10 + 7*x11 + 11*x12 + 13*x13 + 17*x14 + 19*x15, 2*x16 + 3*x17 + 5*x18 +
7*x19 + 11*x20 + 13*x21 + 17*x22 + 19*x23, 2*x24 + 3*x25 + 5*x26 + 7*x27 +
11*x28 + 13*x29 + 17*x30 + 19*x31, 2*x32 + 3*x33 + 5*x34 + 7*x35 + 11*x36 +
13*x37 + 17*x38 + 19*x39, 2*x40 + 3*x41 + 5*x42 + 7*x43 + 11*x44 + 13*x45 +
17*x46 + 19*x47, 23*x0 + 29*x1 + 31*x2 + 37*x3 + 41*x4 + 43*x5 + 47*x6 + 53*x7,
23*x8 + 29*x9 + 31*x10 + 37*x11 + 41*x12 + 43*x13 + 47*x14 + 53*x15, 23*x16 +
29*x17 + 31*x18 + 37*x19 + 41*x20 + 43*x21 + 47*x22 + 53*x23, 23*x24 + 29*x25 +
31*x26 + 37*x27 + 41*x28 + 43*x29 + 47*x30 + 53*x31, 23*x32 + 29*x33 + 31*x34 +
37*x35 + 41*x36 + 43*x37 + 47*x38 + 53*x39, 23*x40 + 29*x41 + 31*x42 + 37*x43 +
41*x44 + 43*x45 + 47*x46 + 53*x47, 59*x0 + 61*x1 + 67*x2 + 71*x3 + 73*x4 +
79*x5 + 83*x6 + 89*x7, 59*x8 + 61*x9 + 67*x10 + 71*x11 + 73*x12 + 79*x13 +
83*x14 + 89*x15, 59*x16 + 61*x17 + 67*x18 + 71*x19 + 73*x20 + 79*x21 + 83*x22 +
89*x23, 59*x24 + 61*x25 + 67*x26 + 71*x27 + 73*x28 + 79*x29 + 83*x30 + 89*x31,
59*x32 + 61*x33 + 67*x34 + 71*x35 + 73*x36 + 79*x37 + 83*x38 + 89*x39, 59*x40 +
61*x41 + 67*x42 + 71*x43 + 73*x44 + 79*x45 + 83*x46 + 89*x47, 97*x0 + 101*x1 +
103*x2 + 107*x3 + 109*x4 + 113*x5 + 127*x6 + 131*x7, 97*x8 + 101*x9 + 103*x10 +
107*x11 + 109*x12 + 113*x13 + 127*x14 + 131*x15, 97*x16 + 101*x17 + 103*x18 +
107*x19 + 109*x20 + 113*x21 + 127*x22 + 131*x23, 97*x24 + 101*x25 + 103*x26 +
107*x27 + 109*x28 + 113*x29 + 127*x30 + 131*x31, 97*x32 + 101*x33 + 103*x34 +
107*x35 + 109*x36 + 113*x37 + 127*x38 + 131*x39, 97*x40 + 101*x41 + 103*x42 +
107*x43 + 109*x44 + 113*x45 + 127*x46 + 131*x47, 137*x0 + 139*x1 + 149*x2 +
151*x3 + 157*x4 + 163*x5 + 167*x6 + 173*x7, 137*x8 + 139*x9 + 149*x10 + 151*x11
+ 157*x12 + 163*x13 + 167*x14 + 173*x15, 137*x16 + 139*x17 + 149*x18 + 151*x19
+ 157*x20 + 163*x21 + 167*x22 + 173*x23, 137*x24 + 139*x25 + 149*x26 + 151*x27
+ 157*x28 + 163*x29 + 167*x30 + 173*x31, 137*x32 + 139*x33 + 149*x34 + 151*x35
+ 157*x36 + 163*x37 + 167*x38 + 173*x39, 137*x40 + 139*x41 + 149*x42 + 151*x43
+ 157*x44 + 163*x45 + 167*x46 + 173*x47, 179*x0 + 181*x1 + 191*x2 + 193*x3 +
197*x4 + 199*x5 + 211*x6 + 223*x7, 179*x8 + 181*x9 + 191*x10 + 193*x11 +
197*x12 + 199*x13 + 211*x14 + 223*x15, 179*x16 + 181*x17 + 191*x18 + 193*x19 +
197*x20 + 199*x21 + 211*x22 + 223*x23, 179*x24 + 181*x25 + 191*x26 + 193*x27 +
197*x28 + 199*x29 + 211*x30 + 223*x31, 179*x32 + 181*x33 + 191*x34 + 193*x35 +
197*x36 + 199*x37 + 211*x38 + 223*x39, 179*x40 + 181*x41 + 191*x42 + 193*x43 +
197*x44 + 199*x45 + 211*x46 + 223*x47, x0 - 1, x1 - 4, x8 - 9, x9 - 16, x16 -
25, x17 - 36, x24 - 49, x25 - 64, x32 - 81, x33 - 100, x40 - 121, x41 - 144]
#==========
print("dimension=",Ideal(J).dimension()) # returns 0
try:
va=Ideal(J).variety()
print(" variety passed")
except Exception as e:
print(" exception in variety ",e) #error skipping text from `)` error
at token `)` and traceback
