# from the theory of proveit.physics.quantum.QPE¶

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.
# import Expression classes needed to build the expression
from proveit import ExprRange, Variable, e
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, frac, one, three, two
from proveit.physics.quantum.QPE import _two_pow_t

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [Neg(Mult(frac(one, Exp(two, one)), _two_pow_t)), one, Neg(e)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, three)]))

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(\frac{1}{2^{1}} \cdot 2^{t}\right), 1, -e\right)| = |\left(1, 2, \ldots, 3\right)|

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 32, 9
6Literal
7ExprTuple10
8Operationoperator: 12
operand: 16
9Operationoperator: 12
operand: 17
10ExprRangelambda_map: 14
start_index: 32
end_index: 15
11ExprTuple16
12Literal
13ExprTuple17
14Lambdaparameter: 21
body: 21
15Literal
16Operationoperator: 19
operands: 20
17Variable
18ExprTuple21
19Literal
20ExprTuple22, 23
21Variable
22Operationoperator: 24
operands: 25
23Operationoperator: 29
operands: 26
24Literal
25ExprTuple32, 27
26ExprTuple31, 28
27Operationoperator: 29
operands: 30
28Literal
29Literal
30ExprTuple31, 32
31Literal
32Literal