# 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 X, c
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, QmultCodomain
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [c], instance_expr = Forall(instance_param_or_params = [X], instance_expr = Equals(Qmult(c, X), ScalarMult(c, X)), domain = QmultCodomain), domain = Complex)
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_{c \in \mathbb{C}}~\left[\forall_{X \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\left(c \thinspace X\right) = \left(c \cdot X\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: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 27
body: 4
3ExprTuple27
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple27, 12
11Lambdaparameter: 28
body: 14
12Literal
13ExprTuple28
14Conditionalvalue: 15
condition: 16
15Operationoperator: 17
operands: 18
16Operationoperator: 19
operands: 20
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple28, 23
21Operationoperator: 24
operands: 26
22Operationoperator: 25
operands: 26
23Literal
24Literal
25Literal
26ExprTuple27, 28
27Variable
28Variable