INTREL <decimal_number>,L
tries to find an exact numeric expression for which <decimal_number>
is an (accurate) approximation.
The PSLQ algorithm by Ferguson and Plouffe (1992) is used.
The main approach is to see <decimal_number> as a root X of an
algebraic equation of nth degree
C0+C1*X+C2*X^2+...+Cn*X^n=0
with integer coefficients C0,C1,C2,...,Cn.
The maximum degree n is set by a specification DEGREE=n (n=1,2,...,20).
The accuracy of approximation is set by EPS, default EPS=1e-12 .
L is the first line for the results (default is CUR+1).
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Example: ACCURACY=16
sqrt(2)=1.4142135623731 DEGREE=2
INTREL 3.4142135623731
X=3.4142135623731 is a root of X^2-4*X+2=0
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By giving a specification CONSTANTS=<matrix_file> values of the first
column, say X1,X2,..., are used instead of powers of X.
Example on the next page:
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Example:
MATRIX C
/// C
1 1
e 2.718281828459045
Pi 3.141592653589793
MAT SAVE C
x=5+2*3.141592653589793-3*exp(1)
x=3.128339821802451
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CONSTANTS=C
INTREL 3.128339821802451
Integer relation for X=3.128339821802451:
Constant Coefficient
X 1
1 -5
e 3
Pi -2
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