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Expression of type Forall

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 U, alpha, n
from proveit.linear_algebra import Norm
from proveit.logic import CartExp, Equals, Forall
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, var_ket_psi
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = Equals(Norm(Qmult(U, var_ket_psi)), alpha), domain = CartExp(Complex, n), condition = 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())
\forall_{\lvert \psi \rangle \in \mathbb{C}^{n}~|~\left \|\lvert \psi \rangle\right \| = \alpha}~\left(\left \|U \thinspace \lvert \psi \rangle\right \| = \alpha\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 31
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 16
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 21
8Literal
9ExprTuple11, 12
10Operationoperator: 26
operand: 18
11Operationoperator: 14
operands: 15
12Operationoperator: 16
operands: 17
13ExprTuple18
14Literal
15ExprTuple31, 19
16Literal
17ExprTuple20, 21
18Operationoperator: 22
operands: 23
19Operationoperator: 24
operands: 25
20Operationoperator: 26
operand: 31
21Variable
22Literal
23ExprTuple28, 31
24Literal
25ExprTuple29, 30
26Literal
27ExprTuple31
28Variable
29Literal
30Variable
31Variable