# 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, X
from proveit.linear_algebra import HilbertSpaces, 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 = Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(A, var_ket_psi), X), domain = Hspace), condition = InSet(Qmult(A), LinMap(Hspace, X))), domain = HilbertSpaces)

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_{\mathcal{H}, X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\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) \in X\right)\right]\right]

In [5]:
stored_expr.style_options()

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()

core typesub-expressionsexpression
0Operationoperator: 19
operand: 2
1ExprTuple2
2Lambdaparameters: 29
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 19
operand: 9
5Operationoperator: 7
operands: 8
6ExprTuple9
7Literal
8ExprTuple10, 11
9Lambdaparameter: 40
body: 12
10Operationoperator: 14
operands: 13
11Operationoperator: 14
operands: 15
12Conditionalvalue: 16
condition: 17
13ExprTuple37, 18
14Literal
15ExprTuple36, 18
16Operationoperator: 19
operand: 22
17Operationoperator: 33
operands: 21
18Literal
19Literal
20ExprTuple22
21ExprTuple23, 24
22Lambdaparameter: 41
body: 26
23Operationoperator: 38
operand: 40
24Operationoperator: 28
operands: 29
25ExprTuple41
26Conditionalvalue: 30
condition: 31
27ExprTuple40
28Literal
29ExprTuple37, 36
30Operationoperator: 33
operands: 32
31Operationoperator: 33
operands: 34
32ExprTuple35, 36
33Literal
34ExprTuple41, 37
35Operationoperator: 38
operands: 39
36Variable
37Variable
38Literal
39ExprTuple40, 41
40Variable
41Variable