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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 A, Conditional, Function, Lambda
from proveit.logic import Equals, InSet
from proveit.physics.quantum import Qmult, var_ket_psi
from proveit.physics.quantum.algebra import Hspace
In [2]:
# build up the expression from sub-expressions
expr = Lambda(var_ket_psi, Conditional(Equals(Qmult(A, var_ket_psi), Function(Qmult(A), [var_ket_psi])), InSet(var_ket_psi, Hspace)))
Out[2]:
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())
\lvert \psi \rangle \mapsto \left\{\left(A \thinspace \lvert \psi \rangle\right) = \left[A\right]\left(\lvert \psi \rangle\right) \textrm{ if } \lvert \psi \rangle \in \mathcal{H}\right..
In [5]:
stored_expr.style_options()
Out[5]:
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0Lambdaparameter: 16
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple16, 10
8Operationoperator: 14
operands: 11
9Operationoperator: 12
operand: 16
10Variable
11ExprTuple17, 16
12Operationoperator: 14
operand: 17
13ExprTuple16
14Literal
15ExprTuple17
16Variable
17Variable