# 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.
# import Expression classes needed to build the expression
from proveit import A, Function, X
from proveit.linear_algebra import LinMap
from proveit.logic import Equals, Forall, 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
sub_expr1 = [var_ket_psi]
sub_expr2 = Qmult(A)
expr = 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)))

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())

\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]

In [5]:
stored_expr.style_options()

Out[5]:
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

Out[6]:
core typesub-expressionsexpression
0Operationoperator: 6
operand: 2
1ExprTuple2
2Lambdaparameter: 30
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 19
operands: 8
6Literal
7ExprTuple9
8ExprTuple25, 10
9Lambdaparameter: 29
body: 11
10Operationoperator: 12
operands: 13
11Conditionalvalue: 14
condition: 15
12Literal
13ExprTuple23, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16Variable
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple29, 23
21Operationoperator: 27
operands: 24
22Operationoperator: 25
operand: 29
23Variable
24ExprTuple30, 29
25Operationoperator: 27
operand: 30
26ExprTuple29
27Literal
28ExprTuple30
29Variable
30Variable