Expression of type Norm

from the theory of proveit.physics.quantum.QPE

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 Variable
from proveit.linear_algebra import Norm, ScalarMult
from proveit.numbers import Exp, Mult, Neg, e, i, pi, two
from proveit.physics.quantum import ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = Norm(ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Variable("_a", latex_format = r"{_{-}a}"))), _phase)), ket1))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left \|\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right \|

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 20 operands: 8
7	Operation	operator: 9 operand: 13
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13
11	Literal
12	Operation	operator: 14 operands: 15
13	Literal
14	Literal
15	ExprTuple	22, 16, 17, 18, 19
16	Literal
17	Literal
18	Operation	operator: 20 operands: 21
19	Literal
20	Literal
21	ExprTuple	22, 23
22	Literal
23	Operation	operator: 24 operand: 26
24	Literal
25	ExprTuple	26
26	Variable