logo

Expression of type ExprTuple

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, ExprTuple, Lambda, X
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.physics.quantum import Qmult, bra_varphi, ket_varphi, var_ket_psi, var_ket_v, varphi
from proveit.physics.quantum.algebra import Hspace
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(var_ket_psi, Conditional(Forall(instance_param_or_params = [varphi], instance_expr = Equals(Qmult(var_ket_psi, bra_varphi), Lambda(var_ket_v, Conditional(ScalarMult(Qmult(bra_varphi, var_ket_v), var_ket_psi), InSet(var_ket_v, Hspace)))), condition = InSet(ket_varphi, Hspace)), InSet(var_ket_psi, 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(\lvert \psi \rangle \mapsto \left\{\forall_{\varphi~|~\lvert \varphi \rangle \in \mathcal{H}}~\left(\left(\lvert \psi \rangle \thinspace \langle \varphi \rvert\right) = \left[\lvert v \rangle \mapsto \left\{\left(\langle \varphi \rvert \thinspace \lvert v \rangle\right) \cdot \lvert \psi \rangle \textrm{ if } \lvert v \rangle \in \mathcal{H}\right..\right]\right) \textrm{ if } \lvert \psi \rangle \in X\right..\right)
In [5]:
stored_expr.style_options()
Out[5]:
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 31
body: 3
2ExprTuple31
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 28
operands: 8
6Literal
7ExprTuple9
8ExprTuple31, 10
9Lambdaparameter: 39
body: 11
10Variable
11Conditionalvalue: 12
condition: 13
12Operationoperator: 14
operands: 15
13Operationoperator: 28
operands: 16
14Literal
15ExprTuple17, 18
16ExprTuple19, 32
17Operationoperator: 33
operands: 20
18Lambdaparameter: 36
body: 22
19Operationoperator: 23
operand: 39
20ExprTuple31, 35
21ExprTuple36
22Conditionalvalue: 24
condition: 25
23Literal
24Operationoperator: 26
operands: 27
25Operationoperator: 28
operands: 29
26Literal
27ExprTuple30, 31
28Literal
29ExprTuple36, 32
30Operationoperator: 33
operands: 34
31Variable
32Variable
33Literal
34ExprTuple35, 36
35Operationoperator: 37
operand: 39
36Variable
37Literal
38ExprTuple39
39Variable