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Expression of type Conditional

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, X
from proveit.linear_algebra import LinMap
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.physics.quantum import HilbertSpaces, Qmult, var_ket_psi
from proveit.physics.quantum.algebra import Hspace
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [var_ket_psi]
sub_expr2 = Qmult(A)
expr = Conditional(Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qmult(A, var_ket_psi), Function(sub_expr2, sub_expr1)), domain = Hspace), condition = InSet(sub_expr2, LinMap(Hspace, X))), And(InClass(Hspace, HilbertSpaces), InClass(X, HilbertSpaces)))
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())
\left\{\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) = \left[A\right]\left(\lvert \psi \rangle\right)\right)\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\right..
In [5]:
stored_expr.style_options()
Out[5]:
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 16
operand: 6
2Operationoperator: 4
operands: 5
3ExprTuple6
4Literal
5ExprTuple7, 8
6Lambdaparameter: 40
body: 9
7Operationoperator: 11
operands: 10
8Operationoperator: 11
operands: 12
9Conditionalvalue: 13
condition: 14
10ExprTuple33, 15
11Literal
12ExprTuple26, 15
13Operationoperator: 16
operand: 19
14Operationoperator: 29
operands: 18
15Literal
16Literal
17ExprTuple19
18ExprTuple35, 20
19Lambdaparameter: 39
body: 21
20Operationoperator: 22
operands: 23
21Conditionalvalue: 24
condition: 25
22Literal
23ExprTuple33, 26
24Operationoperator: 27
operands: 28
25Operationoperator: 29
operands: 30
26Variable
27Literal
28ExprTuple31, 32
29Literal
30ExprTuple39, 33
31Operationoperator: 37
operands: 34
32Operationoperator: 35
operand: 39
33Variable
34ExprTuple40, 39
35Operationoperator: 37
operand: 40
36ExprTuple39
37Literal
38ExprTuple40
39Variable
40Variable