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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, j, k, n
from proveit.logic import And, InSet, NotEquals
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.algebra import n_bit_interval
In [2]:
# build up the expression from sub-expressions
expr = Conditional(NotEquals(NumKet(j, n), NumKet(k, n)), And(InSet(j, n_bit_interval), InSet(k, n_bit_interval), NotEquals(j, k)))
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\{\lvert j \rangle_{n} \neq \lvert k \rangle_{n} \textrm{ if } j \in \{0~\ldotp \ldotp~2^{n} - 1\} ,  k \in \{0~\ldotp \ldotp~2^{n} - 1\} ,  j \neq k\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: 17
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8, 9, 10
6Operationoperator: 12
operands: 11
7Operationoperator: 12
operands: 13
8Operationoperator: 15
operands: 14
9Operationoperator: 15
operands: 16
10Operationoperator: 17
operands: 18
11ExprTuple20, 35
12Literal
13ExprTuple21, 35
14ExprTuple20, 19
15Literal
16ExprTuple21, 19
17Literal
18ExprTuple20, 21
19Operationoperator: 22
operands: 23
20Variable
21Variable
22Literal
23ExprTuple24, 25
24Literal
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28, 29
28Operationoperator: 30
operands: 31
29Operationoperator: 32
operand: 36
30Literal
31ExprTuple34, 35
32Literal
33ExprTuple36
34Literal
35Variable
36Literal