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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, B, Conditional, X, Y
from proveit.linear_algebra import Hspace, LinMap
from proveit.logic import And, InSet
from proveit.physics.quantum import Qmult
In [2]:
# build up the expression from sub-expressions
expr = Conditional(InSet(Qmult(A, B), LinMap(Hspace, Y)), And(InSet(Qmult(A), LinMap(X, Y)), InSet(Qmult(B), LinMap(Hspace, X))))
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\{\left(A \thinspace B\right) \in \mathcal{L}\left(\mathcal{H}, Y\right) \textrm{ if } \left[A\right] \in \mathcal{L}\left(X, Y\right) ,  \left[B\right] \in \mathcal{L}\left(\mathcal{H}, X\right)\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: 13
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8, 9
6Operationoperator: 21
operands: 10
7Operationoperator: 23
operands: 11
8Operationoperator: 13
operands: 12
9Operationoperator: 13
operands: 14
10ExprTuple25, 27
11ExprTuple28, 26
12ExprTuple15, 16
13Literal
14ExprTuple17, 18
15Operationoperator: 21
operand: 25
16Operationoperator: 23
operands: 20
17Operationoperator: 21
operand: 27
18Operationoperator: 23
operands: 24
19ExprTuple25
20ExprTuple29, 26
21Literal
22ExprTuple27
23Literal
24ExprTuple28, 29
25Variable
26Variable
27Variable
28Variable
29Variable