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Math.NET Symbolics
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real 1.0 / 5Q returns 1/5N not 0.2 #73

Closed diluculo closed 4 years ago

diluculo commented 5 years ago

I do some tests to understand how Approximation works by using SymbolicExpression.Parse(infix).

Infix string Expression RealValue Note
1.2 Approximation (Real 1.2) 1.2
1.0 + 1/5 Approximation (Real 1.2) 1.2
1 + 1.0/5 Number 6/5N 1.2 Bug?
1 + 1/5 Number 6/5N 1.2
6/5 Number 6/5N 1.2
6.0/5 Approximation (Real 1.2) 1.2000000000000002
6.0/5 - 6/5 Approximation ... 2.2204460492503131E-16 Machine Epsilon

When an inexact number, or a number with explicit decimal point is given in an expression, it should be approximated. It is strange that real 1.0 / 5Q returns 1/5 not 0.2. The problem is that the active pattern One is used in multiply.

real 1.0 / 5Q -> multiply Approximation(Real 1.0) Number1/5N -> multiply One Number1/5N -> Number1/5N.

cdrnet commented 5 years ago

One could indeed argue the One and MinusOne active patterns should not include approximative values. Maybe also Zero, although the floating point precicion is less of an issue there. A follow up question is then whether we still want 1.0/0.0 to simplify to complex infinity.

diluculo commented 5 years ago

Thanks for quick answer. I got it. There are many hidden rules and layers. I thought simply it would be a good idea to add ExactOne.

cdrnet commented 5 years ago

Yes, either that, or add ApproxOne and change the existing One to no longer include approximative values.

cdrnet commented 4 years ago

I've recently removed the parts where 1.0 was interpreted as 1 and 0.0 was interpreted as 0. I agree with the reasoning.

Infix string Expression RealValue Note
1.2 Approximation (Real 1.2) 1.2
1.0 + 1/5 Approximation (Real 1.2) 1.2
1 + 1.0/5 Approximation (Real 1.2) 1.2 (Fixed)
1 + 1/5 Number 6/5N 1.2
6/5 Number 6/5N 1.2
6.0/5 Approximation (Real 1.2) 1.2
6.0/5 - 6/5 Approximation ... 2.2204460492503131E-16 Machine Epsilon

I think this resolved this issue? Thanks again for bringing this up!