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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, Conditional, Function, X
from proveit.linear_algebra import LinMap
from proveit.logic import Equals, Forall, InSet
from proveit.physics.quantum import Qmult, var_ket_psi
from proveit.physics.quantum.algebra import Hspace
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [var_ket_psi]
sub_expr2 = Qmult(A)
expr = Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qmult(A, var_ket_psi), Function(sub_expr2, sub_expr1)), domain = Hspace), InSet(sub_expr2, LinMap(Hspace, X)))
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())
\left\{\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) = \left[A\right]\left(\lvert \psi \rangle\right)\right) \textrm{ if } \left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)\right..
In [5]:
stored_expr.style_options()
Out[5]:
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()
Out[6]:
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 6
2Operationoperator: 16
operands: 5
3Literal
4ExprTuple6
5ExprTuple22, 7
6Lambdaparameter: 26
body: 8
7Operationoperator: 9
operands: 10
8Conditionalvalue: 11
condition: 12
9Literal
10ExprTuple20, 13
11Operationoperator: 14
operands: 15
12Operationoperator: 16
operands: 17
13Variable
14Literal
15ExprTuple18, 19
16Literal
17ExprTuple26, 20
18Operationoperator: 24
operands: 21
19Operationoperator: 22
operand: 26
20Variable
21ExprTuple27, 26
22Operationoperator: 24
operand: 27
23ExprTuple26
24Literal
25ExprTuple27
26Variable
27Variable