NumberTheory
ThueSolve
solutions to a Thue equation or inequality
Calling Sequence
Parameters
Description
Examples
Compatibility
ThueSolve(expr)
ThueSolve(expr, bound = b)
ThueSolve(expr, vars, bound = b)
expr
-
Thue equation or Thue inequality
vars
set of two names
bound = b
(optional) keyword argument where b is a positive integer; defaults to 10
The ThueSolve function computes all the solutions to a Thue equation or inequality.
Let f⁡x,y be a binary form with integer coefficients and irreducible over the rationals. A binary form is a bivariate polynomial where every term has the same degree. Let m be an integer. A Thue equation has the form f⁡x,y=m and a Thue inequality has the form f⁡x,y≤m.
If the degree of f is less than 3, then isolve is used to find the solutions. Otherwise, there exists a finite number of solutions and this command finds all solutions x,y given the constraint y≤10bound.
with⁡NumberTheory:
ThueSolve⁡x2+x⁢y+y2=19
x=−5,y=2,x=−5,y=3,x=−3,y=−2,x=−3,y=5,x=−2,y=−3,x=−2,y=5,x=2,y=−5,x=2,y=3,x=3,y=−5,x=3,y=2,x=5,y=−3,x=5,y=−2
The variables may be explicitly given.
ThueSolve⁡x3−3⁢x⁢y2+y3=3,x,y
x=−1,y=−2,x=−1,y=1,x=2,y=1
Setting infolevel to 1 or greater will give additional information when solutions do not exist or when solving a Thue inequality.
infolevelThueSolve ≔ 1
infolevelThueSolve≔1
ThueSolve⁡x3−3⁢x⁢y2+y3=2
ThueSolve: try the following constant terms -3, -1, 0, 1, 3
ThueSolve⁡x3+x2⁢y−2⁢x⁢y2−y3≤5
ThueSolve: equality holds for the follow constant terms 0, 1
x=0,y=0,x=−9,y=5,x=−5,y=−4,x=−4,y=9,x=−2,y=1,x=−1,y=−1,x=−1,y=0,x=−1,y=1,x=−1,y=2,x=0,y=−1,x=0,y=1,x=1,y=−2,x=1,y=−1,x=1,y=0,x=1,y=1,x=2,y=−1,x=4,y=−9,x=5,y=4,x=9,y=−5
The NumberTheory[ThueSolve] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
See Also
isolve
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