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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, U, alpha, n
from proveit.linear_algebra import Norm
from proveit.logic import And, CartExp, Equals, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, var_ket_psi
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Norm(Qmult(U, var_ket_psi)), alpha), And(InSet(var_ket_psi, CartExp(Complex, n)), Equals(Norm(var_ket_psi), alpha)))
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 \|U \thinspace \lvert \psi \rangle\right \| = \alpha \textrm{ if } \lvert \psi \rangle \in \mathbb{C}^{n} ,  \left \|\lvert \psi \rangle\right \| = \alpha\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: 12
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 17
4Literal
5ExprTuple7, 8
6Operationoperator: 22
operand: 14
7Operationoperator: 10
operands: 11
8Operationoperator: 12
operands: 13
9ExprTuple14
10Literal
11ExprTuple27, 15
12Literal
13ExprTuple16, 17
14Operationoperator: 18
operands: 19
15Operationoperator: 20
operands: 21
16Operationoperator: 22
operand: 27
17Variable
18Literal
19ExprTuple24, 27
20Literal
21ExprTuple25, 26
22Literal
23ExprTuple27
24Variable
25Literal
26Variable
27Variable