Try extract abs_with_hint

galgebra/metric.py

@@ -9,7 +9,7 @@
 from sympy import (
  diff, trigsimp, Matrix, Rational,
  sqf_list, sqrt, eye, S, expand, Mul,
- Add, simplify, Expr, Function, MatrixSymbol
+ Add, simplify, Expr, Abs, Function, MatrixSymbol
 )
 
 from . import printer
@@ -114,6 +114,35 @@ def collect(A, nc_list):
  return C
 
 
+def abs_with_hint(expr, hint: str) -> Expr:
+ """
+ Heuristics for simplifying the absolute value of an expression with hints.
+ """
+
+ # Case1: expr is numeric
+ if expr.is_number:
+ return Abs(expr)
+ # # Case2: metric is positive definite
+ # if self.Ga.g.is_positive_definite:
+ # return expr
+ # Case3: expr is nonnegative
+ if (expr >= 0) == True: # noqa: E712
+ return +expr
+ # Case4: expr is nonpositive
+ if (expr <= 0) == True: # noqa: E712
+ return -expr
+
+ # Case5: expr's sign is unknown, so use `hint`.
+ if hint == '0':
+ return Abs(expr)
+ elif hint == '+':
+ return +expr
+ elif hint == '-':
+ return -expr
+ else:
+ raise ValueError("hint must be '0', '+', or '-'.")
+
+
 def square_root_of_expr(expr, hint='0'):
  """
  If expression is product of even powers then every power is divided by two
@@ -151,7 +180,7 @@ def square_root_of_expr(expr, hint='0'):
  return sqrt(abs(expr))
  else:
  coef *= f ** (n / S(2)) # Positive sqrt of the square of an expression
- return coef
+ return abs_with_hint(coef)
 
 
 def symbols_list(s, indices=None, sub=True, commutative=False):

galgebra/mv.py

@@ -1280,28 +1280,12 @@ def norm2(self, hint: str = '0') -> Expr:
  Euclidean.
  """
  quadform = self.qform() # the quadratic form at `self`
- # Case1: quadform is numeric
- if quadform.is_number:
- return Abs(quadform)
+
  # Case2: metric is positive definite
  if self.Ga.g.is_positive_definite:
  return quadform
- # Case3: quadform is nonnegative
- if (quadform >= 0) == True: # noqa: E712
- return +quadform
- # Case4: quadform is nonpositive
- if (quadform <= 0) == True: # noqa: E712
- return -quadform
-
- # Case5: quadform's sign is unknown, so use `hint`.
- if hint == '0':
- return Abs(quadform)
- elif hint == '+':
- return +quadform
- elif hint == '-':
- return -quadform
- else:
- raise ValueError("hint must be '0', '+', or '-'.")
+
+ return metric.abs_with_hint(quadform, hint)
  # ## GSG code ends ###
 
  # ## GSG code starts ###

test/.nbval_sanitize.cfg

@@ -54,5 +54,5 @@ replace: {Python }
 regex: \{SymPy \}(\d+\.\d+(\.\d+)?(\.dev)?)
 replace: {SymPy }
 # \text{GAlgebra }0.5.0
-regex: \{GAlgebra \}(\d+\.\d+(\.\d+)?)
+regex: \{GAlgebra \}(\d+\.\d+(\.\d+)?(-dev)?)
 replace: {GAlgebra }