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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 Conditional, X, c
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, QmultCodomain
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [X], instance_expr = Equals(Qmult(X, c), ScalarMult(c, X)), domain = QmultCodomain), InSet(c, Complex))
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_{X \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\left(X \thinspace c\right) = \left(c \cdot X\right)\right) \textrm{ if } c \in \mathbb{C}\right..
In [5]:
stored_expr.style_options()
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()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple24, 8
7Lambdaparameter: 25
body: 10
8Literal
9ExprTuple25
10Conditionalvalue: 11
condition: 12
11Operationoperator: 13
operands: 14
12Operationoperator: 15
operands: 16
13Literal
14ExprTuple17, 18
15Literal
16ExprTuple25, 19
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operands: 23
19Literal
20Literal
21ExprTuple25, 24
22Literal
23ExprTuple24, 25
24Variable
25Variable