logo

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, Lambda, X
from proveit.linear_algebra import Hspace, LinMap
from proveit.logic import Forall, InSet
from proveit.physics.quantum import Qmult, var_ket_psi
In [2]:
# build up the expression from sub-expressions
expr = Lambda(A, Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(A, var_ket_psi), X), domain = Hspace), InSet(Qmult(A), LinMap(Hspace, X))))
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())
A \mapsto \left\{\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) \in X\right) \textrm{ if } \left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 25
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operand: 7
3Operationoperator: 18
operands: 6
4Literal
5ExprTuple7
6ExprTuple8, 9
7Lambdaparameter: 26
body: 11
8Operationoperator: 23
operand: 25
9Operationoperator: 13
operands: 14
10ExprTuple26
11Conditionalvalue: 15
condition: 16
12ExprTuple25
13Literal
14ExprTuple22, 21
15Operationoperator: 18
operands: 17
16Operationoperator: 18
operands: 19
17ExprTuple20, 21
18Literal
19ExprTuple26, 22
20Operationoperator: 23
operands: 24
21Variable
22Variable
23Literal
24ExprTuple25, 26
25Variable
26Variable