Cristóvão wrote :
I propose a generic function mapexpression in order operate in the tree
of the expression.
You can use it over leaf (ie the numbers or the variables) or over
functions (by the fctfct parameter)
I like this function because we can use this same function for numerical
transforms (for Christavo)
and rewrite rules (with trigonometric rules).
There are 2 fuzzy cases for operator add and mul because the
fct(*operand) doesn't work for add and mul.
import operator
def mapexpression (expr, fctleaf, fctfct, param, level, addDepth=0,
mulDepth=0) :
def mapex (expr, depth) : # a very local function
opor = expr.operator()
opands = expr.operands()
if (opor == None) :
return fctleaf(expr,param) # a leaf in the expression tree
if (opor == operator.add) : # recursive call thru sum
opands = map (lambda ex : mapex (ex, depth+addDepth), opands)
return add (opands)
if (opor == operator.mul) : # recursive call thru mul
opands = map (lambda ex : mapex (ex, depth+mulDepth), opands)
return mul (opands)
if (level == -1) or (level[-1] >= depth) : # recursive call over
operands
opands = map (lambda ex : mapex (ex, depth+1), opands)
if level == -1 or depth in level : # root of the subtree must be
changed
return fctfct (opor, opands, param)
return opor (*opands) # opands may or maynot be changed by a
recursive call
return mapex (expr, 0)
def nn (ex, p) :
if ex._is_numeric() or ex==pi: return ex.n(prec=p)
else : return ex
sage: mapexpression (sin(5*pi/7)+exp(i*pi/13),nn, lambda x,y,z:x(*y),20,-1)
1.7528 + 0.23932*I
Method __.n() doesn't work over partial numerical formula, but this
mapexpression allows this.
Francois
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