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Expression of type Lambda

from the theory of proveit.physics.quantum.algebra

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, X, c
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, QmultCodomain
In [2]:
# build up the expression from sub-expressions
expr = Lambda(c, Conditional(Forall(instance_param_or_params = [X], instance_expr = Equals(Qmult(X, c), ScalarMult(c, X)), domain = QmultCodomain), InSet(c, Complex)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
c \mapsto \left\{\forall_{X \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\left(X \thinspace c\right) = \left(c \cdot X\right)\right) \textrm{ if } c \in \mathbb{C}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 26
body: 2
1ExprTuple26
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple26, 10
9Lambdaparameter: 27
body: 12
10Literal
11ExprTuple27
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple19, 20
17Literal
18ExprTuple27, 21
19Operationoperator: 22
operands: 23
20Operationoperator: 24
operands: 25
21Literal
22Literal
23ExprTuple27, 26
24Literal
25ExprTuple26, 27
26Variable
27Variable